Find the vertex and the extreme value of the function f (x) = -x^2+x+2.....

Question

Find the vertex and the extreme value of the function
f (x) = -x^2+x+2
The extreme value is the maximum or minimum value of a quadratic function. Be sure to leave your answer as a reduced fraction.

What is the vertex?

What is the extreme value?

Answer 1

f(x) = -x²+x+2

This is a parabola that opens downward to the f(x) value

at the vertex will be the maximum.

 

The vertex is at (-b/2a, f(-b/2a))

a=-1, b=1

 

-b/2a = -1/(-2) = 1/2

f(1/2) = -(1/2)² + 1/2 + 2

          = -1/4 + 5/2

          = 9/4 or 2 1/4

 

Vertex = (1/2, 9/4)

Extreme value = maximum at 9/4