using complete sentences explain how to find the minimum value for each for each function and and determine which function has the smallest y value
f(x) = 3x^2 + 12x + 16
And
g(x) = 2sin (2x-pi) +4

- anonymous

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- anonymous

##### 1 Attachment

- anonymous

@jim_thompson5910 I'm pretty sure the minimum point for f(x) is (-2, 4). Is that correct?

- jim_thompson5910

yep the min for f is y = 4 when x = -2
ie the min f(x) = 4 occurs at the point (-2,4)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

Okay how to we find g(x)?

- jim_thompson5910

when does sin(x) have a minimum?

- anonymous

I don't know

- jim_thompson5910

look at the unit circle
what is the lowest point on it?

- anonymous

(0, -1)?

- jim_thompson5910

what is the corresponding angle

- jim_thompson5910

I'll be right back in a few minutes

- anonymous

(0, 1)? and okay

- jim_thompson5910

I'm back
no look at where it shows the angle theta

- jim_thompson5910

what angle theta is where (0,-1) is located?

- anonymous

I don't know what it is. I'm confused

- jim_thompson5910

look at this
http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/1024px-Unit_circle_angles_color.svg.png
and tell me what the angle is

- anonymous

I don't know I'm lost..

- jim_thompson5910

do you see the 270 degrees?

- anonymous

Yes

- jim_thompson5910

so that's why sin(270 degrees) = -1
or sin(3pi/2 radians) = -1

- jim_thompson5910

the min occurs when sin(x) = -1, ie when x = 3pi/2
so you have to determine when 2x-pi is equal to 3pi/2

- jim_thompson5910

2x-pi = 3pi/2
what is x equal to?

- anonymous

0?

- jim_thompson5910

you should get x = 5pi/4

- jim_thompson5910

I see a shortcut though

- jim_thompson5910

they just want the min y value
sin( anything ) has a min of -1
so 2sin (2x-pi) +4 turns into 2*(-1) +4 when you replace all of "sin..." with the smallest it can get, which is -1

- anonymous

This is confusing to me.. I'm trying to understand it but it's a lot of info.. I'm not good with trigonometry

- jim_thompson5910

2*(-1) +4 turns into 2, so this is the smallest that g(x) can get

- jim_thompson5910

notice on the wavy graph, the lowest points have a y coordinate of y = 2

- anonymous

Yea I noticed that. So y=2 but what is x? Do we need to know x?

- jim_thompson5910

they just want to know the smallest output of the function

- anonymous

Okay. So g(x) has the smallest minimum?

- jim_thompson5910

yes

- jim_thompson5910

and you can see that on your graph you posted

- anonymous

Yeah I see that now haha. Do you mind helping with one more?

- jim_thompson5910

alright

- anonymous

Prove: \[\sin \theta-\sin \theta \times \cos^2 \theta = \sin^3 \theta\]

- jim_thompson5910

hint: factor out sin(theta)

- jim_thompson5910

only alter the left side
do not change the right side

- anonymous

So it would be \[\cos^2 \theta = \sin^3 \theta?\]

- jim_thompson5910

you should have
\[\Large \sin(\theta)\left(1-\cos^2(\theta)\right) = \sin^3(\theta)\]

- jim_thompson5910

then try to do something with the 1-sin^2

- anonymous

How would you get 1-sin^2?

- jim_thompson5910

oops

- jim_thompson5910

I meant 1-cos^2

- anonymous

Would you multiply |dw:1433476582158:dw|

- jim_thompson5910

nope

- jim_thompson5910

there's an identity you use for 1-cos^2

- jim_thompson5910

hint: sin^2 + cos^2 = 1

- anonymous

So 1-cos^2 would become sin^2

- jim_thompson5910

yep

- anonymous

Thank you so much

- jim_thompson5910

you're welcome

- anonymous

Wait how did you get the 1 again?

Looking for something else?

Not the answer you are looking for? Search for more explanations.