Question

find the maximum y-value on the graph of y=f(x)
f(x)= -x^2 + 2x +1
the maximum y-value is y =

Answer 1

hi, to find the maximum value you need to differentiate the equation twice, if the 2nd derivative is <0, then you have a maximum point.

Answer 2

\[\frac{ dy }{dx }= -2x+2\]

Answer 3

\[\frac{ d^2y }{ dx^2 }=-2\]

Answer 4

so you can see that your 2nd derivative is a negative value, hence you have a maximum point

Answer 5

so the maximum value would be -2?

Answer 6

i think what the question is asking you is to draw the graph and figure the maximum value from the graph

Answer 7

i am drawing it now i will send you the graph

Answer 8

there is no graph, it is just asking for a maximum value from that equation

Answer 9

sorry i was on the phone

Answer 10

yes i read your question again

Answer 11

ind the maximum y-value on the graph of y=f(x)
f(x)= -x^2 + 2x +1

Answer 12

your teacher has specified the method

Answer 13

they want you to figure the answer from the graph

Answer 14

so this means you have to factorize your equation and sketch it

Answer 15

so you need to find the vertex of the equation

Answer 16

i will show you how to do that

Answer 17

\[y= \frac{ 4ac-b^2 }{ 4 }\]

Answer 18

sorry i wrote your equation the wrong way

Answer 19

\[f(x) = -x^{2}+2x+1\]

Answer 20

can you confirm

Answer 21

(x+1)(x+1)?

Answer 22

i know the answer

Answer 23

but i want you to see how to get that answer

Answer 24

your y value is -2 but if i ask you to prove that graphically can you do so?

Answer 25

no

Answer 26

well what you do is that you have to draw it

Answer 27

as you did you factorize the equation then find the x values

Answer 28

then you substitute or plug the x values in the main equation to find y

Answer 29

you can have a look at the graph

Answer 30

you can draw that in ms word

Answer 31

i can't come up with the answer, thank you anyways

Answer 32

wait

Answer 33

the answer is -2 for max y value

Answer 34

are you there?

Answer 35

yes

Answer 36

do you know how to draw a function in general?

Answer 37

like making a table of x/y values

Answer 38

ok

Answer 39

now if you do that you'll see the max y value graphically

Answer 40

another way to that is the following method

Answer 41

set x= 0 to see were your graph intersect with the y-axis

Answer 42

then set y=0 to see where your graph intersect with the x-axis

Answer 43

to find the maximum value of y, use the vertex equation

Answer 44

\[y= \frac{ 4ac-b^2 }{ 4 }\]

Answer 45

and to find x of the maximum y

Answer 46

\[x=-\frac{ b }{2a }\]

Answer 47

okay thank you