Question

Type the correct answer in each box. Use numerals instead of words. What are the x-intercept and vertex of this quadratic function? g(x)=-5(x-3)^2

Answer 1

The x-intercept is (3,0).

The vertex of the function is (3,0).

Explanation:

Given : Function
`g(x)=-5(x-3)^2`

To find : What are the x-intercept and vertex of this quadratic function?

Solution :

Function
`g(x)=-5(x-3)^2`

The x-intercept is when g(x)=0.

i.e.
`-5(x-3)^2=0`

Divide by -5 both side,

`(x-3)^2=0`

Taking root both side,

`x-3=0`

Add 3 both side,

`x=3`

The x-intercept is (3,0).

The general vertex form of the quadratic function is
`y=a(x-h)^2+k`

where, (h,k) is the vertex

Compare the given function
`g(x)=-5(x-3)^2`

a=-5 , h=3 and k=0

The vertex of the function is (3,0).