Question

Find the equation of a parabola that has a vertex of (3,-1)and has a y intercept of(0,-8)

Answer 1

The equation of a parabola in standard form y = -7/9 x^2 +14/3 x - 8.

Explanation:

The equation of a parabola in vertex form is

y = a(x -h)^2 + k

Given:

(h, k) = (3, -1)

y-intercept = (0, -8)

Now plug in h = 3, k = -1, x =0 and y = -8 in the vertex form and find the value of "a"

-8 = a( 0 - 3)^2 - 1

-8 = 9a - 1

-7 = 9a

a = -7/9

a = -7/9

Now plug in a = -7/9

y = -7/9 (x - 3)^2 -1

y = -7/9(x^2 - 6x + 9) - 1

y = -7/9x^2 + 14/3x -7 -1

y = -7/9 x^2 +14/3 x - 8

Thank you.