Finding the Equation of a Parabola Given Three Points

www.greenemath....
/ mathematicsbyjgreene
In this lesson, we will learn how to find the equation of a parabola given three points on the parabola. To perform this action, we will use the three points given to set up a system of linear equations in three variables. To obtain our three equations, we will simply plug in for x and y in the equation y = ax^2 + bx + c. This will allow us to solve for the three unknowns: a, b, and c. Once we have solved for a, b, and c, we can plug into the standard form of a parabola: y = ax^2 + bx + c and obtain our equation.

[@chisomagannajide7601]

Thank you so much!!!! I was stuck on a question like this and your video helped me out!!!! Thanks so much!!!!!

[@Greenemath]

You are so welcome!

[@angiecole830]

my 3 equations are c=-1 16a-4b+c=1 4a-2b+c=-3 my points are (0,-1) (-4,-1) (-2,-3) How would I get my end equation because when I subtracted the 2nd and 3rd equations I got 12a-2b=2 then I would have to subtract c=-1 but there is no to subtract from. Sorry if this a dumb equation i am just a little stuck how to get my end equation in vertex form?

[@Greenemath]

Alright so let's take it from the top. y = ax^2 + bx + c (0, -1) -1 = c or c = -1 (-4, -1) 16a - 4b + c = -1 Yours here says = 1, but the y-value is -1 (-2, -3) 4a - 2b + c = -3 So here's the equations to work with: 16a - 4b + c = -1 4a - 2b + c = -3 c = -1 Since you know that c is -1 just replace it in the top two 16a - 4b + (-1) = -1 16a - 4b = 0 4a - 2b + -1 = -3 4a - 2b = -2 Okay so now we have an easy system to solve: 16a - 4b = 0 Divide each part by 4: 4a - b = 0 Other one: 4a - 2b = -2 Divide each part by -2: -2a + b = 1 Okay so now: 4a - b = 0 -2a + b = 1 You see how you have opposite signs on b, so we can use elimination: 4a - b - 2a + b = 1 2a = 1 a = 1/2 4(1/2) - b = 0 2 - b = 0 b = 2 So your a is 1/2, b is 2, and c is -1 y = 1/2 x^2 + 2x - 1. If you are confused on any steps let me know.

[@angiecole830]

@@Greenemath OMG you are a life saver! Thank you so much! I am very grateful for your help! Have an awesome day! Also i hope you get more subscribers because you are under rated

[@Greenemath]

@@angiecole830 I'm glad it was helpful, let me know if you have other questions. 😎

[@angiecole830]

@@Greenemath Will do!

[@earlfan2138]

Thank you for the video!

[@Greenemath]

You are very welcome! :)

[@izzy_haines]

Sorry I am still confused, my points are (-2,18), (3,-2), and (1,0). I got to the simplified equations part but I am just lost when it comes to making the fourth and fifth equation. Equations : 1. 4a - 2b + c = 18 2. 9a + 3b + c = -2 3. a + b + c = 0 I thought I did it right but I keep getting the answer wrong. Thank you in advance!

[@izzy_haines]

Okay I got my fourth and fifth equation : 4. 3a - 3b = 18 5. 8a + 2b = -2 But I don't know what do after that. I tried to follow the steps in the video but I keep getting the answer wrong.

[@Greenemath]

Did you figure it out?

[@laroujensen1094]

Thanks

[@Greenemath]

You are welcome Larou

[@hulaanmo2132]

Cant Equation 4: 3a-3b=24 be simplified into a-b=8 to make things easier?? But either way the answer will be the same, anyways thanks for this

[@Greenemath]

Yes, of course you can if you want to. As you correctly pointed out, the answer will be the same either way.