Answer:
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
[tex]y=a(x-h)^{2}+k[/tex]
where
a is a coefficient
(h,k) is the vertex
In this problem we have
(h,k)=(6,-5)
substitute
[tex]y=a(x-6)^{2}-5[/tex]
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
[tex]175=a(0-6)^{2}-5[/tex]
[tex]175=36a-5[/tex]
[tex]36a=180[/tex]
[tex]a=5[/tex]
substitute
[tex]y=5(x-6)^{2}-5[/tex]
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
[tex]0=5(x-6)^{2}-5[/tex]
[tex]5(x-6)^{2}=5[/tex]
simplify
[tex](x-6)^{2}=1[/tex]
square root both sides
[tex]x-6=(+/-)1[/tex]
[tex]x=6(+/-)1[/tex]
[tex]x=6(+)1=7[/tex]
[tex]x=6(-)1=5[/tex]
therefore
The x-intercepts are (5,0) and (7,0)
