Question

Using the completing-the-square method, find the vertex of the function f(x) = –2x^2 + 12x + 5 and indicate whether it is a minimum or a maximum and at what point.


A. Maximum at (–3, 5)

B. Minimum at (–3, 5)

C. Maximum at (3, 23)

D. Minimum at (3, 23)

Answer 1

Answer:

Option C. Maximum at  $(3,23)$

Step-by-step explanation:

we have

$f(x)=-2x^{2}+12x+5$

Completing the square

$f(x)-5=-2x^{2}+12x$

$f(x)-5=-2(x^{2}-6x)$

$f(x)-5-18=-2(x^{2}-6x+9)$

$f(x)-23=-2(x^{2}-6x+9)$

$f(x)-23=-2(x-3)^{2}$

$f(x)=-2(x-3)^{2}+23$ --------> quadratic equation in vertex form

The vertex is the point $(3,23)$

This is a vertical parabola open downward

therefore

The vertex is a maximum