Question

do I have to complete the square on the following problem in order to find the min or max?
ate whether the function f (x ) = -2x^ 2 - 20x + 15 has a maximum or minimum
value and state the value of the maximum or minimum.

Answer 1

There are several different things you can do to find the min or max. If you don't already know the general shape of the graph, I recommend that you graph it first. You probably know that it is a parabola, but you may now know if it has a min or max yet.

Answer 2

I know its a parabola with a min

Answer 3

could I turn it into standard form and use the completing the square method?

Answer 4

Yes, you could definitely do that

Answer 5

great thank you =)

Answer 6

That's one way to do it.

Answer 7

Do you know which value of standard form would give the max?

Answer 8

Oh, I guess I gave it away.

Answer 9

It is a parabola with a max, not min

Answer 10

https://www.desmos.com/calculator/boulocbgwa

Answer 11

isn't this a min because of the - by the 2x^2?

Answer 12

the negative just means the parabola opens downward

Answer 13

that's right! I got it mixed up and if the parabola opens upward then its a positive next to the 2x^ and its a min?

Answer 14

so the max number is the last number?

Answer 15

The maximum value of the parabola occurs at its peak and corresponds with the numerical position along the y-axis.

Answer 16

If you complete the square, then you would get the same thing. But when you complete the square, you would have to know what you are doing.

Answer 17

There's another method you could use that doesn't require graphing or completing the square.

Answer 18

for some reason I like completing the square =)

Answer 19

I see. So... demonstrate to me how you plan to go about completing the square.

Answer 20

k I will be back in a few min

Answer 21

-2x-20x+15
-2(x+10x)+15
-2(x+10x+25)+15+50
-2(x+5)^2+65
okay so my max value is 65 .... I was flipping what a min and a max earlier lol

Answer 22

Yes that is correct but if you're going to write it make sure to include both sides of the equal sign. Someone else might want to read your work and it is proper practice to include the complete formulas and equations when expressing your self mathematically.

Answer 23

you mean the f(x) =

Answer 24

Yes, that's what I mean. When you post on OS, you're not just doing it for yourself, but for others as well. That's what the "Open" part of Open Study sort of alludes to.

Answer 25

okay ^O^

Answer 26

I mean, even if you did it this way:

f(x) = -2x^2-20x+15
= -2(x^2+10x)+15
= -2(x^2+10x+25)+15+50
= -2(x+5)^2+65

That would be acceptable.