Question

WIll give medal and fan!!!
What is the maximum or minimum value of the function? What is the range?

y = –2x2 + 32x –12 (1 point)
maximum: 116
range: y 116
maximum: –116
range: y –116
maximum: 116
range: y 116
maximum: –116
range: y –116

Answer 1

this is an opening down parabola, and we know that it has no absolute minimum, since it will be going infinitely down on both ends.

Answer 2

Yes

Answer 3

you can find the vertex of this, and this will be the absolute maximum of the function.
need help findning the vertex?

Answer 4

Yes.

Answer 5

\(\large\color{black}{ y = -2x^2 + 32x -12 }\)

first go ahead an factor out of \(\large\color{black}{ -2 }\) for me please.

Answer 6

Okay!

Answer 7

what do you get, after doing this?

Answer 8

http://www.mathportal.org/calculators/quadratic-equation/quadratic-function-grapher.php

Answer 9

are you offering me a calculator to fill in values so that I can factor it? I know how to factor it:)
I want to see though how you would factor it out of -2.

Answer 10

take the derivative: -4x+32 and set it equal to zero.
-4x+32=0
-4x=-32
x=8
Take second derivative: -4 which indicates the curve is concave down. Indicated it is a max.
Maximum 116 at x=8
Range: (-inf, 116)

Answer 11

but I don't know what the open would be?

Answer 12

you don't need the derivative for an absolute maximum of a parabola.

Answer 13

i dont get it.

Answer 14

you know since the coefficient of x^2 is negative that it is going down. This means that it will have the absolute maximum, but not absolute minimum.

you can just find the vertex of it

Answer 15

the vertex will be the absolute maximum.

Answer 16

\(\large\color{black}{ y = -2x^2 + 32x -12 }\)

please factor out of -2 for me, (you should know how to do it, if you are already mentioning derivatives)

Answer 17

you derivatives are correct, but there is no need in doing this.

Answer 18

a = -2x^2

Answer 19

a =-2x^2 ? what does this mean?

Answer 20

I am sorry I don't know how to do it :(((

Answer 21

if you can't factor the \(\large\color{black}{ y = -2x^2 + 32x -12 }\)
out of -2 (on the right hand side of the equation)

then I don't know how to do. You want to tell me you are capable of finding the derivative and of applying it to find the absolute maximum, but can't simply factor?

Answer 22

I forgot hwo tooo. ]