If you're looking for detailed, step-by-step answers, you've come to the right place. Hope it helps. 8 = a(3 - 2)^2 + 3 \text{ or } 8 = a(1)^2 + 3, University of Georgia: Writing Quadratic Equations. We note that the "a" value is positive, resulting in a "legs up" orientation, as expected. I felt sick in Pre-Calc yesterday while they were reviewing this and wasn't up to asking the teacher to repeat everything cuz it didn't make sense at that moment but this really helps ! They can be used to calculate areas, formulate the speed of an object, and even to determine a product's profit. Using this formula, all we . I thought you had to divide the 6 by the 9, except that produces a 3. Fitting a quadratic through 5 points, goal is to find the maximum. 1989) reserve the term for a quartic equation having no cubic term, i.e., a quadratic equation in x^2. But on my math homework, I we are working with conic sections and parabolas. Mathematics is the study of numbers, shapes, and patterns. This is super helpful but just wondering, in the systems of equations example, why do multiply the last line by 2? (a) Write down the turning point of the graph y=x - 2x - 3. let the equation of the quadratic function be: y = a x 2 + b x + c. since the curve passes through the points ( 3, 0), ( 2, 0), and ( 0, 30) . (This gives the blue parabola as shown below). find the equation of the tangents to a quadratic curve through the point $(-7,1)$ 1 Conic sections ( coordinates of the point of intersection of tangents with the curve ) We cannot determine or but for a given we find that and, plugging back into we get that . Instead of x, you can also write x^2. I am a 41 year old who is about to study maths and physics at uni for the first time; stuff like this is fantastic. Thanks for such a useful information. of the parabola on the graph, and plug it into the vertex form of a quadratic equation. Get better grades with tutoring from top-rated private tutors. How to get the equation of a parabola given x intercepts quadratic vertex and y intercept find from graph function finding chilimath roots an ex. This is not so straightforward from observations of a graph. $$L(x) = {y_1}\cdot{x - x_2 \over x_1 - x_2}\cdot{x - x_3 \over x_1 - x_3}+ {y_2}\cdot{x - x_1 \over x_2 - x_1}\cdot{x - x_3 \over x_2 - x_3}+ {y_3}\cdot{x - x_1 \over x_3 - x_1}\cdot{x - x_2 \over x_3 - x_2}$$, you can make the ansatz $$y=a^2+bx+c$$ and plug in all your points in this equation Direct link to kit wing's post instead of the formula, m, Posted 9 years ago. The possible x-values will be the x-intercepts; where you line crosses the x-axis. Substitute the last ordered pair and the values of b and c into the general equation. The quadratic equation whose roots are , , is x 2 - ( + )x + = 0. $$y_3=ax_3^2+bx_3+c$$ for $a,b,c$, Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. In the standard form. We'll use that as our 3rd known point. Use the given point (-1, 3), which says y is 3 for x equal to -1. It turns out there are an infinite number of parabolas passing through the points (2,0) and (1,0). I wish the camera feature was a bit more accurate, but other than that, it couldnt get any better, so it's not necessarily cheating if it helps you learn too, so far really good. example Peace! Sometimesb2{b}^{2}b2is preceded by a negative sign, which means you are squaring all of b, even if it is negative. Graphing calculators will probablynotbe equal to the precision of the quadratic formula. Hopefully this proof helps you understand why: There are several ways to derive the quadratic formula, but the simplest is by using completing the square. Apart from these lengthy calculations, our free online quadratic regression calculator determines the same results with each step properly performed within seconds. Work through it. Possible answer: Do I substitute in the value of x and y (in this case x=2, y=3) into the equation y = x^2 +bx + c to get 3 = 2^ + 2b + c (although I thought c would be 3 as this is the point where the curve crosses the y-axis? Which becomes when expanded: Hi, So far, so good. i.e a trinomial? Use the given point (-1, 3), which says y is 3 for x equal to -1. These are designed to handle interpolation. using the amount of revenues and expenses, we can determine if based on the number of staff and encounters. No need to be a math genius, our online calculator can do the work for you. what if the curve has three x-intecepts? First we factor the equation. If you need to cheat in a math test, use this app. In solving quadratics, you help yourself by knowing multiple ways to solve any equation. Substituting for x and y: 3 = a(-1 - 3)2 - 1 = 3 = a(-4)2 Substituting for x and y: 3 = a(-1 - 3)2 - 1 = 3 = a(-4)2. Looking for detailed, step-by-step answers? The more data points you give Excel (especially near extremes like maxima, minima and x- and y-intercepts), the closer the resulting polynomial will be to your given graph. The first derivative is found by differentiating the function. This method will allow one to "fit" a curve to any number of data points. y=\goldD {a} (x-\blueD h)^2+\greenD k y = a(x h)2 + k Direct link to Bentley S.'s post Im here, Posted 5 years ago. Check. []. Finding the equation of a parabola given certain data points is a worthwhile skill in mathematics. [] Murray Bourne explains step by step How to find the equation of a quadratic function from its graph. That is, y = ax + bx + c y = ax + bx + c From these we obtain Cheers everyone!! The idea is to use the coordinates of its vertex (maximum point, or minimum point) to write its. This gives us y = a(x 1)2. 1) Find Quadratic Equation from 2 Points In order to find a quadratic equation from a graph using only 2 points, one of those points must be the vertex. A word with quad" in it usually implies four of something, like a quadrilateral. Were not big fans of you memorizing formulas, but this one is useful (and we think you should learn how to derive it as well as use it, but thats for the second video!). Thanks!!! @Evogod: Feel free to ask more about this in the IntMath Forum. We know that a quadratic equation will be in the form: y = ax 2 + bx + c Our job is to find the values of a, b and c after first observing the graph. Direct link to Estelle Pretorius's post If the coefficient of x^2, Posted 5 years ago. . Connect and share knowledge within a single location that is structured and easy to search. x = [- (-7) ( (-7) 2 - 4 (1) (10))] / (2 (1)) = [ 7 (49 - 40) ] / 2 = [ 7 (9) ] / 2 = [ 7 3 ] / 2 @ABC: Every parabola passes through at least one of the axes. how to graph a parabola ? I found your graphs and explanations very helpful. (1) While some authors (Beyer 1987b, p. 34) use the term "biquadratic equation" as a synonym for quartic equation, others (Hazewinkel 1988, Gellert et al. To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. In order to find a quadratic equation from a graph, there are two simple methods one can employ: using 2 points, or using 3 points. I like the app because it helps me with my homework or work in general and it doesn't glitch which is very good. @Peter: Actually, if there are 3 intercepts, it's a quadrinomial. @Simon: You'll need to use the "Vertex Method" as detailed in the article. In algebra, a quadratic equation is any polynomial equation of the second degree with the following form: ax 2 + bx + c = 0 where x is an unknown, a is referred to as the quadratic coefficient, b the linear coefficient, and c the constant. Enter the points in cells as shown, and get Excel to graph it using "X-Y scatter plot". Calculate a quadratic function given the vertex point. Consider a quadratic equation in standard form: a {x}^ {2}+bx+c=0 ax2 + bx + c = 0. The quadratic formula helps you solve quadratic equations, and is probably one of the top five formulas in math. Quadratic Formula: x = bb2 4ac 2a x = b b 2 4 a c 2 a. @John: Yes, that would do it. For an example, let the vertex be (2, 3). Direct link to Karyn Williams's post I do not enjoy math and I, Posted 5 years ago. NOTE: You can mix both types of math entry in your comment. This set of data is a given set of graph points that make up the shape of a parabola. @Jaahnavi I think you mean "vertex points", right? In the same form of $y=$, what is the formula for a quadratic equation with 3 points? Look no further our experts are here to help. $$y\ =\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}x+\frac{\left(y_1+y_2-\left(x_1\left(\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}\right)+x_2\left(\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}\right)\right)\right)}{2}$$ http://www.sscc.edu/home/jdavidso/Math/Catalog/Polynomials/Fifth/FifthDegreeB.html how would I figure out the function? [duplicate], Getting a standard form quadratic from a set of points ($3$ points), We've added a "Necessary cookies only" option to the cookie consent popup, Mathematics behind intersection points of two lines using quadratic equation, Fitting a quadratic polynomial to two points such that it is always concave downward. What if your originalbisalreadynegative? I am in algebra 1 and got stuck on a homework problem. If you are trying to find the zeros for the function (that is find x when f(x) = 0), then that is simply done using quadratic equation - no need for math software. A quadratic equation has two solutions if the discriminant b^2 - 4ac is positive. And we have to match the graph to it's corresponding equation. Writing Quadratic Equations. Under the square root bracket, you also must work with care. Learn how to find the equation of a quadratic (parabola) given 3 points in this video by Mario's Math Tutoring.0:21 General Form of a Quadratic (Parabola)0:37 Writing a System of 3 Equations to Solve for a, b, c2:07 Solving the System by Elimination2:53 Putting a, b, c Back Into the EquationRelated Videos:Solving Systems of 3 Equations Using Eliminationhttps://youtu.be/UcYbFN49uGcUsing the TI84 to Find Equation of a Parabola Given 3 Pointshttps://youtu.be/lNXoDsuPmCsLooking to raise your math score on the ACT and new SAT? You could use MS Excel to find the equation. Another option could be to approach an existing entity that's doing interesting things (New York's Museum of Mathematics comes to mind) and offer your services as a researcher. We can set each expression equal to0and then solve for x: Comparing our example,x2+5x+6=0{x}^{2}+5x+6=0x2+5x+6=0, to the standard form of the quadratic equation (which can also just be called the quadratic), we get these values: Now we can use those in the quadratic formula and check, since we already know our answers are-2and-3: The ever-reliable quadratic formula confirms the values ofxas-2and-3. Use the given point (-1, 3), which says y is 3 for x equal to -1. There are multiple ways to reduce stress, including exercise, relaxation techniques, and healthy coping mechanisms. and i need to form a quadratic equation based on that could you pls help me out with it.. Hello Abhishek. Quadratic Equation in Standard Form: ax 2 + bx + c = 0 Quadratic Equations can be factored Quadratic Formula: x = b (b2 4ac) 2a When the Discriminant ( b24ac) is: positive, there are 2 real solutions zero, there is one real solution negative, there are 2 complex solutions How did the value of a become 2? HTML: You can use simple tags like , , etc. Set either form to zero and solve the equation to find the points where the parabola crosses the x-axis. (If there are no other "nice" points where we can see the graph passing through, then we would have to use our estimate.). @Mike: Good question! Hi Kathryn and thanks for your input. I'm wondering whether a role like a research assistant in some existing mathematics education research may be the way to go for you. Here are some of them: In this example, the blue curve passes through (0, 1) on the y-axis, so we can simply substitute x = 0, y = 1 into y = a(x 1)2 as follows: So our quadratic function for this example is. c is the y-intercept (ie the height at the point where x=0) This will give you insight to the answer of @DrSonnhardGraubner. Now he explains how to find a mirror point using an example with sample values. Mathematics is the study of patterns and relationships between numbers, shapes, and other mathematical concepts. The formula to find the roots of the quadratic equation is x = [-b (b 2 - 4ac)]/2a. It can be very useful to solve equations and stuff but it's too specialised on that, but math app I hope you can fix the camera but that doesn't matter cause I can just type. Maybe someone who reads this could invent one? Instead of x, you can also write x^2. To approximate a Sine curve with a quardric equation to generate a signal for a computer music system. With just two of the parabola's points, its vertex and one other, you can find a parabolic equation's vertex and standard forms and write the parabola algebraically. No factors of-3add to-7, so you cannot use factoring. But there are an infinite number of parabolas that contain these two points because we can make the a coefficient any real number. When using the quadratic formula, you must be attentive to the smallest details. The vertex there fore would be (13.13,y?) In this video the tutor shows how to find the mirror point using a quadratic equation. So the y-intercept is 19. Another approach to the parabola problem, which may be of particular interest to calculus students, is that for a parabola to be the graph of y=ax^2+bx+c: Math is a way of solving problems by using numbers and equations. System of Equations method; In this tutorial, you'll see how to solve such a system by combining the equations together in a way so that one of the variables is eliminated. I am to find a equation of a parablo given the vertex (7,-2) and one x-intercept (4,0). When a quadratic equation is graphed, it forms a parabola. The idea is to use the coordinates of its vertex (maximum point, or minimum point) to write its Determine math. And it's still a nice day! regression of data points for portfolio analysis. Calculate a quadratic function given the vertex point Computing a quadratic function out of three points. In order to find a quadratic equation from a graph, there are two simple methods one can employ: using 2 points, or using 3 points. The square of a negative is a positive, sob2{b}^{2}b2will always be a positive value. ), Yes x with a little 2 to its top right is x to the power of 2, but for future reference when typing x to the power of 2 on the computer the convention is to use the "^" symbol to say "to the power of". However, with a little practice and perseverance, anyone can learn to love math! Videos Arranged by Math Subject as well as by Chapter/Topic. I mean I have heard of so called Octic Equations which are of the form: In 1827, a mathematician by the last name of Abel proved that there is no way to make an analogous equation past the 4th degree. It only takes a minute to sign up. Figure 2: Quadratic formula. Why are trials on "Law & Order" in the New York Supreme Court? Get math help online by speaking to a tutor in a live chat. Free quadratic functions calculator. Math is a challenging subject for many students, but with practice and persistence, anyone can learn to figure out complex equations. If you're looking for fast answers, you've come to the right place. 2 02 Quadratic Equations. The quadratic formula x=\dfrac {-b\pm\sqrt {b^2-4ac}} {2a} x = 2ab b2 4ac It may look a little scary, but you'll get used to it quickly! Solve for c. For instance, 19 = -(-1.5c + 4.5) - c + 5 + (-1.5c + 4.5)(3) + c simplifies to c = 1. Please reply soon. Can you help me understand what he means? In example 3 we need to find extra points. In your example, y = 2(x-3)^2+1, when x = 0, y = 19. I found this website and it is so wonderful! Keep up with the latest news and information by subscribing to our email list. In math, a quadratic equation is a second-order polynomial equation in a single variable. Say I have this quintic polynomial graph without the function. Two cloud shapes down and one to go. Polynomials (algebraic expressions with many terms) can have linear, square, and cubic values. Again, your page is interesting and excellent for H.S and college students. i have a question where the curve is a parabola passing through the origin a point is given its neither the max nor min it's on the curve the point is (1,2) and then the curve again cuts through the x axis at (6,0) What if the curve not passing through any of axis. Substituting 2 for h and 3. order now. But once again, we are not even trying to find an "x". May God bless and guide you! Given just 2 points, to find a linear equation, this is the formula: Use the quadratic formula to check factoring, for instance. We will now prepare a table for the roots of "X" which are "x1" and "x2", and . @Maheera: Glad it helped! (We'll assume the axis of the given parabola is vertical.). There's nothing more frustrating than being stuck on a math problem. I have no feedback here but really, This app works with me since 2015 when I saw the first ads on IG and im still using it until now, if you are a student you need to check this out, even my maths teacher can't explain as nicely, knows everything I need accept some graphing. Create the equations by substituting the ordered pair for each point into the general form of the quadratic equation, ax^2 + bx + c. Simplify each equation, then use the method of your choice to solve the system of equations for a, b and c. Finally, substitute the values you found for a, b and c into the general equation to generate the . As the y intercept was at -3, could we not simply use this to determine the proper equation: The last ordered pair is (3, 19), which yields the equation: 19 = a(3^2) + 3(3) + 1. Thanks, once again, for emphasizing "real" math (for both utility and understanding). Substitute the first pair of values into the general form of the quadratic equation: f(x) = ax^2 + bx + c. Solve for a. Thank you so much for this page.. if you mean find the solution, yes, you would get -3 and 1. That is, we can do it with software or without. Direct link to Daniel Rendall's post does x2 = x to the power , Posted 9 years ago. @Mick: Thanks for the positive feedback. Nothing magic about it - when x does equal zero, we are on the y-axis. Instead of x, you can also write x^2. Direct link to Adithi J's post Good question! How to find the equation of a logarithm function from its graph? So I would get y= 2^2 + 2b + 3). I do not enjoy math and I need some help. 20+ tutors near you & online ready to help. First note, Posted 9 years ago. Thanks. In this example, let the point be (3, 8). Plug in 0 for x and see if the equation gives you -3, the y -intercept. Leave as is, rather than writing it as a decimal equivalent(3.16227766), for greater precision. Here is the appropriate section: Plane Analytical Geometry. Substituting 2 for h and 3 for k into, Substitute the point's coordinates for x and y in the equation. Mathepower calculates the quadratic function whose graph goes through those points. I agree that this is the kind of thing that schools and texts need to concentrate more on. Does the above equation represent a parabola? For example, (1, 5), (2,11) and (3,19). I have some physical experiments done at various locations. I appreciate the simple images to go along with the explanations, that also helped a lot. Sometimes it is easy to spot the points where the curve passes through, but often we need to estimate the points. More advanced: I want to fit parabola equation at any axis of symmetry. A parabola is the locus of points equidistant from a Substitute any ordered pair and the value of c into the general equation. This gives the black curve shown. The above is an equation (=) but sometimes we need to solve inequalities like these: . Hint: If Parabolas have two equation forms - standard and vertex. y=ax Solve math With a little practice, anyone can learn to solve math problems quickly and efficiently. Why is this the case. Think: the negative of a negative is a positive; so-bis positive! There is simply no way to make an analogous equation for any polynomial of degree y for y>4, not enough operations are defined by the rules of mathematics. There are many different ways to solve a system of linear equations. of the parabola on the graph, and plug it into the vertex form of a quadratic equation. Everything, from-bto the square root, is over2a. This is a mathematical educational video on how to find extra points for a parabola. Use the standard form y = ax2 + bx +c and the 3 points to write 3 equations with, a, b, and c as the variables and then solve for the variables. Direct link to blackbean798's post Is anyone here in 2022, Posted 4 months ago. I just you to install this for free. For convenience let us assume that we have 3 points (1,5), (3,2) & (5,3). Thanks a lot! Take a look! In the vertex form, y = a (x - h)^2 + k y = a(x h)2 +k the variables h and k are the coordinates of the parabola's vertex. How to find equation of quadratic function with two points - This site allow users to input a Math problem and receive step-by-step instructions on How to find. Note: We could also make use of the fact that the x-value of the vertex of the parabola y = ax2 + bx + c is given by: Here's an example where there is no x-intercept. Solve for a. The University of Georgia; Writing Quadratic Equations; J. Wilson. For example, 11 = (-b + 4)(2^2) + b(2) + 1 simplifies to b = 3. Are you still struggling? Use the standard form of a quadratic equation y=ax2+bx+c y = a x 2 + b x + c as the starting point for finding the equation through the three points. Its such a convenient and reliable tool, this app should help education worldwide. Everytime i do this i get an infinite loop. I am confused about one thing.If the y-intercept is (4.2), would we replace the 4 in place if the x instead of zero.just making sure the 0 is not used every time. How do I find a quadratic equation given 2 points and no vertex? Given Three Points In the next example that you can see here, we're given. Calculate a quadratic function given the vertex point Enter the vertex point and another point on the graph. One of the activities in my "Blue Meanies" game (at http://qpr.ca/math/applets/meanies/ )asks students to "guess" the equation of a parabola through three points by imagining the curve and using its geometry (in various ways) to determine the equation. Where does this (supposedly) Gibson quote come from? For example, classify the stationary points of y = 3 + 6 2 + 9 + 4 using the first derivative.. Math can be tricky, but there's always a way to find the answer. To find the unique quadratic function for our blue parabola, we need to use 3 points on the curve. Quadratic equations have the general form: ax 2 + bx + c = 0 If the "a" coefficient is greater than 0, the parabola is "U-shaped" and if the "a" coefficient is less than 0, the parabola is "-shaped". Posted in Mathematics category - 17 May 2011 [Permalink]. . Does ZnSO4 + H2 at high pressure reverses to Zn + H2SO4? Then right click on the curve and choose "Add trendline" Choose "Polynomial" and "Order 2". I want to know for a set of paired x and y values how do I find vortex points (using f(x)=a(x-h)^2+k formula)? @Harry: Thanks for your kind comments about this IntMath post. I'll try to find time to write an article on this. Substitute the third ordered pair and the values of a and b into the general equation. For instance, you can substitute (1, 5) into the equation to yield 5 = a(1^2) + b(1) + 1, which simplifies to a = -b + 4. This is a good question because it goes to the heart of a lot of "real" math. I would like to know how to find the equation of a quadratic function from its graph, including when it does not cut the x-axis. Then apply the quadratic formula. . This app has been really great for helping me with my gcse work. Great app almost always right, this helped me bring my grade up from a D+ to a A- In algebra. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Good luck with your studies! a = 1, b = 6, c = 8 f(x) = x2 6x + 8 This is the final equation in the article: f(x) = 0.25x^2 + x + 2. - Interactive Mathematics, How to find the equation of a quadratic function from its graph, Use simple calculator-like input in the following format (surround your math in backticks, or, Use simple LaTeX in the following format. http://www.sscc.edu/home/jdavidso/Math/Catalog/Polynomials/Fifth/FifthDegreeB.html, https://www.intmath.com/forum/plane-analytic-geometry-37/. Thanks for the calculus-based approach, Alan. But you know to try the quadratic formula, with these values: Quadratic equations are actually used every day. How could we go about figuring out the equation of other types of graphs? I have tried hard but found none. If you're having trouble understanding a math question, try clarifying it by rephrasing it in your own words. (Most "text book" math is the wrong way round - it gives you the function first and asks you to plug values into that function.). Or maybe it does have but the image provided is limited so I can't see it touching anything and I can't substitute. For your second question, see also the 2 links I gave in my reply to Leah, above. Google Photos) then put the link to it here. Direct link to Anna's post Could you extend this qua, Posted 6 years ago. if we fit these points generally they fit on parabola with axis of symmetry on Y axis but i want to fit these points in parabola with axis of symmetry on X Axis and 2 points of the parabola intersecting on Y Axis. The Quadratic Formula Calculator finds solutions to quadratic equations with real coefficients. The equation that describes the graph with points (1, 5), (2, 11) and (3, 19) is x^2 + 3x + 1. Ferrari was the first to develop an . May be of interest to some of you, see this simple how-to obtain curve fitting equation from graph image / published graph at: https://pocketengineer.wordpress.com/2016/04/02/how-to-obtain-curve-fitting-equation-from-graph-image-published-graph/. Using the vertex form of a parabola f(x) = a(x - h)2 + k where (h,k) is the vertex of the parabola The axis of symmetry is x = 0 so h also, We can use the vertex form to find a parabola's equation. The y -intercept is (0, -3). GeoGebra will give us the equation of a parabola, but you need to know the focus and directrix first. Substitute your known values and you'll end up with a system of equations, similar to the one in the article. where the curve crosses the x-axis. GeoGebra can be used very easily to find the equation of a parabola: given three points, A, B, C input the command FitPoly[{A, B, C}, 2]. What if there are no points touching the x-axis and y-axis? Now you can also solve a quadratic equation through factoring, completing the square, or graphing, so why do we need the formula? Finding a quadratic function with a parabola. in mathematics from the City University of New York and a masters from Long Island University. Thanks! Plugging this into the second equation gives or which is the same as . https://www.intmath.com/plane-analytic-geometry/4-parabola.php, https://www.intmath.com/quadratic-equations/4-graph-quadratic-function.php. Still a great one if you're struggling in math, but most of it is Perfect. The quadratic formula is used to solve quadratic equations. We already have a quiz Mnday! Just go about it the same as I did int he article: start with y = ax^2 + bx + c and substitute in your 3 points, then solve. Can anyone help? By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. we are trying to find the equation of the parabola. I did some digging and found a GeoGebra applet (no longer available) which draws a parabola through 3 points. In this article, we review how to graph quadratic functions. We can see on the graph that the roots of the quadratic are: x = 2 (since the graph cuts the x-axis at x = 2); and, x = 1 (since the graph cuts the x-axis at x = 1.). How to Write Quadratic Equations Given a Vertex & Point We can use the vertex form to find a parabola's equation. To find the quadratic functions f(x) = ax^2 + bx + c whose graphs contain the points (1,0) and (3,0) we can evaluate f at 1 and 0 to find \begin{eqnarray*} f(1) Clarify mathematic problem In mathematics, an equation is a statement that two things are equal. Just give me a few minutes and I'll have the answer for you. Direct link to nkfonseka's post Start from the beginning , Posted 7 years ago. Use the x-intercepts for 3 known values, then choose one other point on the curve and finally, set up a system of 3 equations in 3 unknowns and solve them. If asked for the exact answer (as usually happens) and the square roots cant be easily simplified, keep the square roots in the answer, e.g. The general form of a quadratic equation is y=ax^2+bx+c . Explanation: Because the question specifies a function, we must discard the form that is not a function: x = ay2 +by + c and use only the form: y = ax2 +bx +c [1]
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