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

Answer:

The x-intercept is (3,0).

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

Step-by-step 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).