Question

Find the x-intercepts of the parabola with

vertex (6,-5) and y-intercept (0,175).
Write your answer in this form: (x1,71),(x2,42).
If necessary, round to the nearest hundredth.
Enter the correct answer.

Answer 1

The x-intercepts are (5,0) and (7,0)

Explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

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

where

a is a coefficient

(h,k) is the vertex

In this problem we have

(h,k)=(6,-5)

substitute

`y=a(x-6)^(2)-5`

Find the coefficient a

with the y-intercept (0,175) substitute the value of x and the value of y in the equation

For x=0, y=175

`175=a(0-6)^(2)-5`

`175=36a-5`

`36a=180`

`a=5`

substitute

`y=5(x-6)^(2)-5`

Find the x-intercepts

Remember that the x-intercepts are the values of x when the value of y is equal to zero

For y=0

`0=5(x-6)^(2)-5`

`5(x-6)^(2)=5`

simplify

`(x-6)^(2)=1`

square root both sides

`x-6=(+/-)1`

`x=6(+/-)1`

`x=6(+)1=7`

`x=6(-)1=5`

therefore

The x-intercepts are (5,0) and (7,0)