Mathematics: Find the x-intercepts of the parabola with vertex (6,-5) and y-intercept (0,175). write your answer in this form: (x1,,42). if necessary, round to the nearest hundredth. enter the correct answer.

Find the x-intercepts of the parabola with vertex

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12.03.2022

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

Step-by-step 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)

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