Question

Functions f(x) and g(x) are shown below:


Using complete sentences, explain how to find the maximum value for each function and determine which function has the largest maximum y-value.

Answer 1

@amistre64

Answer 2

@SarahEZZMcK

Answer 3

Do you know how to find the maximum value of a quadratic (function f)?

Answer 4

That is what I am struggling with. Would you help me understand this?

Answer 5

sure...for a quadratic, the maximum (or minimum if it's opening up) will occur at the vertex.

Answer 6

there are several ways to find the vertex, but in your case, here, it's made easier because the function is in a good form

Answer 7

whenever you have a quadratic in the form \[f(x)=a(x-h)^{2}+k\]
the vertex will be at the point (h, k)

*notice the sign of the value of h changes...

So, can you tell me what the vertex of your function f is?

Answer 8

(6,3)

Answer 9

perfect

Answer 10

so the maximum y-value for function f is 3

Answer 11

now do you do the same thing for g(x) even though it has cos and pi in it?

Answer 12

now, for function g, cosine has a maximum value of 1...so replace the \[cos(2x-\pi)\] with 1 and simplify to get the maximum value for g.

Answer 13

ok. :) got it. Thanks for all your help!!

Answer 14

np :)

Answer 15

so it would be six correct?