Question

Functions f(x) and g(x) are shown below:
f(x) = 3x2 + 12x + 16
g(x)= 2*sin(x-pi) or see attached graph
Using complete sentences, explain how to find the minimum value for each function and determine which function has the smallest minimum y-value.

Answer 1

@Mehek14 @myininaya @ParthKohli

Answer 2

Please help

Answer 3

you can see the minimum value of g(x) from the graph

f(x) is a parabola and we can find its minmum value by converting to the vertex form

Answer 4

3x^2 + 12x + 16
= 3(x^2 + 4x) + 16

now we complete the square on x^2 + 4x
can you do that?

Answer 5

Isnt it just -2, and no im sorry i dont know how to complete the square

Answer 6

yes it is -2
how did you get that ?

Answer 7

By using the formula \[-b/2a\]

Answer 8

\[-12/2\times3=-2\]

Answer 9

ooops sorry the minimum value is not -2 . -2 is the value of x when f(x) is a minimum.

IYes -b/2a is another way of finding this

To find mimimum you plug in x = -2 into f(x)

Answer 10

So then its 4?

Answer 11

yes thats correct

Answer 12

Ok, thanks, then how do i find the minimum of the sine graph/function

Answer 13

there are 2 ways
read it off the graph
OR

usie the fact that the minimum value of the sine is -1

Answer 14

Oh ok thank you

Answer 15

so

sin(x - pi) = -1

then 2 sin (x - pi) = ?

Answer 16

-1?

Answer 17

2 * -1

Answer 18

-2

Answer 19

So the minimum for g(x)=-2?

Answer 20

yes if sin x = -1 then 2 sin x = -2

Answer 21

yes

Answer 22

Ok then g(x) has the smallest minimum y-value?