Question

Find the maximun y-value on the graph of y=f(x). f(x)=-x^2+2x+2

Answer 1

You must select words more carefully. Words mean things.

You have defined y = f(x). Therefore, it makes no sense to sak "What is y?" You just defined it.

If you copied this accurately, you should complain to the author.

Anyway, how do you propose that we might find a solution? Perhaps a 1st Derivative? Maybe a 2nd Derivative? What say you?

Answer 2

change -x^2 +2x+2 into completed square form

Answer 3

can u?

Answer 4

no how do I do that

Answer 5

So, algebra it is, then. You MUST know how to complete the square. Utilize this principle: \((a+b)^{2} =a^{2} +2ab+b^{2}\)

How do you apply that to your right-hand expression?

Answer 6

notsu re

Answer 7

-x^2+2x+2
-(x^2-2x)+2
-{(x)^2 - 2*x*1 + 1^2 - 1^2 } +2
-(x-1)^2 +1+2
-(x-1)^2+3

Answer 8

So, f(x)=-(x-1)^2+3
right?

Answer 9

right

Answer 10

Now, (x-1)^2>=0
u know it?

Answer 11

is that y

Answer 12

y=f(x)=-(x-1)^2+3

Answer 13

so y=(x-1)^2+3

Answer 14

NO

Answer 15

U missed the -ve sign

Answer 16

where

Answer 17

y=-(x-1)^2+3

Answer 18

oh gotsa

Answer 19

So,
(x-1)^2>=0
-(x-1)^2<=0
-(x-1)^2+3<=3
y<=3

Answer 20

thanks

Answer 21

So, the max value of y is 3
got it?

Answer 22

yes