# How do you find the equation for the parabola with the given Vertex (4,-1), point (-2,35)?

##### 1 Answer

Aug 24, 2015

Find the equation of the parabola

Ans: y = 9x^2 - 72x + 143

#### Explanation:

Equation of the parabola :

Vertex (4, -1)

x-coordinate of vertex:

y-coordinate of vertex f(4) = -1

f(4) = 16a + 4b + c = - 1 (2)

The parabola passes at point (-2, 35), then f(-2) = 35

f(-2) = 4a + 2b + c = 35 (3)

We have 3 equations to find 3 unknowns a, b, and c.

(3) gives:

->

(2) gives:

-4a = - 36. -->

Equation:

Check: x of vertex --> x = -b/2a = 72/18 = 4 OK

y of vertex: f(4) = 9(16) - 72(4) + 142 = 144 - 288 + 143 = - 1 OK