Question

Find the x-intercepts of the parabola with vertex (-2,20) and y-intercept (0,0). Write your answer in this form: (x1,y1),(x2,y2). If necessary, round to the nearest hundredth.

Answer 1

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

Step-by-step explanation:

We would apply the equation of parabola in the vertex form:

y = a(x-h)² + k

vertex (-2, 20) represents (h, k)

y-intercept (0, 0) represents (x, y)

Inserting the above in the formula:

0 = a(0 - (-2))² + 20

0 = a(0+2))² + 20

0 = a(2)² + 20

0 = a(4) + 20

-20 = 4a

divide both sides by 4:

-20/4 = 4a/4

-5 = a

The equation becomes:

y = -5(x-h)² + k

y = -5(x+2)² + 20

To get the x-intercept, we would replace y with 0

0 = -5(x+2)² + 20

-20 = -5(x+2)²

-20/-5 = -5(x+2)²/-5

4 = (x+2)²

square root both sides:

`\begin{gathered} \sqrt[]{4}\text{ = }\sqrt[]{(x+2)^(2)} \\ \pm2\text{ = x+ 2} \\ x+2\text{ = }\pm2 \\ x\text{ = -2}\pm2 \\ x\text{ = -2 + 2 or -2 - 2} \\ x\text{ = 0 or x = -}4 \end{gathered}`

The answer in the form (x1,y1),(x2,y2) is (-4, 0), (0, 0)