Question

What is the equation of the parabola that has its vertex at (8,-1) and a y-intercept of

(0, -17)?
A) y= -1/4(X + 8)2 - 1
B) y = -1/4(x - 3)2 + 1
C) y= -1/4(x - 3)2 - 1
D) y=1/44* - 8)2 - 1

Answer 1

Explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex ad a is a multiplier

Here (h, k ) = (8, - 1 ) , then

y = a(x - 8)² - 1

To find a substitute (0, - 17 ) into the equation

- 17 = a(0 - 8)² - 1 ( add 1 to both sides )

- 16 = 64a ( divide both sides by 64 )

`(-16)/(64)` = a , that is

a = -
`(1)/(4)`

y = -
`(1)/(4)`(x - 8)² - 1 ← equation of parabola