33.5k views
0 votes
The functions f(x) = -(x-1)^2 + 5 and g(x) = (x+2)^2 - 3 have been rewritten using the completing-the-square method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.

User Rusmir
by
7.7k points

1 Answer

1 vote

Answer:

a) f(x) has a maximum vertex

b) g(x) has a minimum vertex

Explanation:

The function


p(x) = a(x - h)^(2) + k

has its vertex at (h,k).

If a>0, then (h,k) is a minimum vertex.

If a<0, then (h,k) is a maximum vertex.

The first function is


f(x) = - (x - 1)^(2) + 5

a=-1<0, therefore the vertex (1,5) is the maximum point.

The second function is


g(x) = {(x + 2)}^(2) - 3

a=1>0, therefore the vertex (-2,-3) is a minimum point.

User Nikolay Marinov
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories