Question

Which of the following is an equation in the form y = ax2 + bx + c of the parabola shown in the graph? Show your work.

A. y = −5x2 − 20x − 65
B. y = −5x2 − 20x − 20
C. y = −x2 − 27x − 90
D. y = −5x2 + 20x + 25

Answer 1

Option D. y = – 5x² + 20x + 25

Explanation:

We'll begin by obtaining the solutions to the equation from the graph. This can be obtained as follow:

The solutions are simply the values through which the graph cuts the x-axis.

The solutions are x = – 1 and 5.

Next, we shall obtain the equation for the graph as follow:

x = – 1 Or x = 5

x + 1 = 0 or x – 5= 0

(x + 1) (x – 5) = 0

Expand

x(x – 5) + 1(x – 5) = 0

x² – 5x + x – 5 = 0

x² – 4x – 5 = 0

Multiply through by 5

5x² – 20x – 25 = 0

Rearrange

0 = 0 – (5x² – 20x – 25)

= – 5x² + 20x + 25

Thus, the equation is:

y = – 5x² + 20x + 25