Question

Algebra 2 Question-
Using complete sentences, explain how to find the minimum value for each function and determine which function has the smallest minimum y-value.
f(x) = 3x2 + 12x + 16
g(x) = 2 * sin(x - pi)

Answer 1

Have you done any calculus - finding derivatives?

Answer 2

no

Answer 3

This is trig?

Answer 4

Yeah

Answer 5

Thought so.

Answer 6

im really bad at trig

Answer 7

you can find the minimum value of the first function by completing the square

Answer 8

I'm in the same boat as you, buddy. I'm taking it rn. ;-; You probably know more about it than me. Good luck to you!

Answer 9

Can you please explain to me how to do that?

Answer 10

OK
You have to convert the function to the vertex form

a(x - b)^2 + c where c will be the minimum value

f(x) = 3x^2 + 12x + 16

divide first 2 terms by 3

= 3(x^2 + 4x) + 16

now x^2 + 4x = (x + 2)^2 - 4 so we have

3[(x + 2) ^2 - 4] + 16

= 3(x + 2)^2 + 16 - 12

= 3(x + 2)^2 + 6

so the minimum value is 4.

Answer 11

* penultimate line should read + 4 NOT + 6

Answer 12

so minimum value of f(x) is 4
and you can read the minimum value of g(x) from the graph

Answer 13

Thanks that really did help me out a lot. I appreciate it

Answer 14

To find the minimum value of g(x) without the graph you use the fact that the minimum value of the sine function is -1 . So since you have 2 sin (x - pi) the minimum value is 2*-1.

Answer 15

yw