## The vertex of a parabola is (-1.5, -12.5), and its y-intercept is (0, -8). The x-intercepts of the parabola are __(1)__ and __(2)___.<

Question

The vertex of a parabola is (-1.5, -12.5), and its y-intercept is (0, -8).
The x-intercepts of the parabola are __(1)__ and __(2)___.

(-2,0)
(-4,0)
(2,0)
(4,0)

(-1,0)
(2,0)
(1,0)
(-2,0)

0

## Answers ( No )

1. The vertex form of the equation of the parabola is:

y = A(x – h)^2 + k

Where h and k are the x and y – coordinates of the vertex.

In this case h = – 1.5 and k = – 12.5, so you know that the equation of this parabola is:

y = A(x + 1.5)2 – 12.5

The y-intercept is the y-value when x = 0, so you know:

– 8 = A(0 + 1.5)^2 – 12.5, from which you can solve for A:

– 8 = A (1.5)^2 – 12.5

A(1.5)^2 = – 8 + 12.5

A = 4.5 / (1.5)^2 = 2.

And now you have the equation of the parabola: y = 2(x + 1.5)^2 – 12.5

The x-intercepts are the x-values when y = 0

=> 2(x + 1.5)^2 – 12.5 = 0

=> (x + 1.5)^2 = 12.5 / 2

(x + 1.5)^2 = 6.25

=> (x + 1.5) = +/- √6.25

(x + 1.5) = +/- 2.5

=> x = -1.5 +/- 2.5

=> x = – 1.5 + 2.5 = 1 and x = -1.5 – 2.5 = – 4

=> (1,0) and (-4,0)

Answer: (-4,0) and (1,0)