Question

HELP PLEASE IM STUCK:
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.

Maximum at (–3, 5)
Minimum at (–3, 5)

Answer 1

Vertex form is \(\Large y = a(x-h)^2+k\)
The vertex of that equation is \(\Large (h,k)\)


From \(\Large -2x^2 + 12x + 5\) we see that \(\Large a = -2, b = 12, c = 5\)

Plug the values of 'a' and 'b' into the formula
\[\Large h = \frac{-b}{2a}\]
to find the value of h. Tell me what you get

Answer 2

Oh, I thought you already know the answer to this. Hmmm.

Answer 3

so it would be A? @jim_thompson5910

Answer 4

why maximum?

Answer 5

because it increases

Answer 6

you're looking at the graph I'm guessing?

Answer 7

yes

Answer 8

do you know how to determine without the graph? by just looking at the value of 'a'

Answer 9

no, but can you just determine by looking at the graph?

Answer 10

well let's say we don't have a graphing calculator

since 'a' is a negative number, this means that the parabola opens downward like this



a good way to remember this is to think "The value of 'a' is negative. Negative means sad, so we have a sad face graph"

Answer 11

ok

Answer 12

and of course, at the peak of this "sad face graph" is the vertex. Which in this case, is the max