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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

User Bhumi
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1 Answer

5 votes

Answer:

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).

User Donavon Yelton
by
8.0k points

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