contestada

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)

Respuesta :

calculista

Answer:

Option C. Maximum at  [tex](3,23)[/tex]

Step-by-step explanation:

we have

[tex]f(x)=-2x^{2}+12x+5[/tex]

Completing the square

[tex]f(x)-5=-2x^{2}+12x[/tex]

[tex]f(x)-5=-2(x^{2}-6x)[/tex]

[tex]f(x)-5-18=-2(x^{2}-6x+9)[/tex]

[tex]f(x)-23=-2(x^{2}-6x+9)[/tex]

[tex]f(x)-23=-2(x-3)^{2}[/tex]

[tex]f(x)=-2(x-3)^{2}+23[/tex] --------> quadratic equation in vertex form

The vertex is the point [tex](3,23)[/tex]

This is a vertical parabola open downward

therefore

The vertex is a maximum

Otras preguntas