Using the completing-the-square method, find the vertex of the function f(x) = –2xsquared + 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)

Question

Using the completing-the-square method, find the vertex of the function f(x) = –2xsquared + 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)

akshvas · Answer

You can easily find the vertex by differentiating the function once and putting it to 0

akshvas · Answer

or you can transform this function to the standard parabola X^2=4BY

linseylou88 · Answer

how do you do this?

akshvas · Answer

$$y=-2(x ^{2}-6x+9-9-\frac{ 5 }{ 2 }) = -2[(x-3)^{2}-\frac{ 23 }{ 2 }]$$

akshvas · Answer

$$(x-3)^{2}=(-1/2)(y-23)$$

akshvas · Answer

There would be a maximum and no minimum since it's a downward facing parabola.

akshvas · Answer

is the answer C ?

akshvas · Answer

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