Does anyone want to help me with math for a fan and medal?

- anonymous

Does anyone want to help me with math for a fan and medal?

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- anonymous

@jim_thompson5910

- anonymous

1. For f(x) = x2 and g(x) = (x − 3)2, in which direction and by how many units should f(x) be shifted to obtain g(x)?

- anonymous

2. David kicks a soccer ball off the ground and in the air, with an initial velocity of 35 feet per second. Using the formula H(t) = −16t2 + vt + s, what is the maximum height the soccer ball reaches?

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## More answers

- jim_thompson5910

post one at a time please

- anonymous

sorry

- jim_thompson5910

hint for #1
when going from f(x) to f(x-h), the graph is shifted |h| units to the right if h is positive
when going from f(x) to f(x-h), the graph is shifted |h| units to the left if h is negative

- anonymous

its positive so...

- jim_thompson5910

yes, the x-h matches up with x-3
h = 3

- anonymous

ohh ok i got it

- anonymous

it wouldn't be -3 tho?

- anonymous

@jim_thompson5910

- jim_thompson5910

no, think of it as like the opposite
h-3 ----> shift 3 units to the RIGHT

- jim_thompson5910

|dw:1443491690709:dw|

- anonymous

ohhhh ok!

- jim_thompson5910

|dw:1443491701434:dw|

- anonymous

here are the choices... the answer would be B then right?

- anonymous

Left 3 units
Right 3 units
Up 3 units
Down 3 units

- jim_thompson5910

what's really going on is the entire xy axis is being shifted 3 units to the left, the f(x) stays still giving the illusion it's moving 3 units to the right

- anonymous

oh so would the answer be B or A? @jim_thompson5910

- jim_thompson5910

like I said and drew, f shifts 3 units to the right

- anonymous

Oh thank you!

- anonymous

For the second, here are the choices

- anonymous

17.9 feet
18.2 feet
18.7 feet
19.1 feet

- jim_thompson5910

`2. David kicks a soccer ball off the ground and in the air, with an initial velocity of 35 feet per second. Using the formula H(t) = −16t2 + vt + s, what is the maximum height the soccer ball reaches?`
what are `v` and `s` in this case?

- anonymous

s is 0?

- anonymous

v is 35

- anonymous

@jim_thompson5910

- jim_thompson5910

yes on both

- jim_thompson5910

so `H(t) = -16t^2 + vt + s` turns into `H(t) = -16t^2 + 35t + 0` which is really `H(t) = -16t^2 + 35t`

- anonymous

how do i solve without t though?

- jim_thompson5910

I'm going to replace every t in ` -16t^2 + 35t + 0` with x
so we have ` -16x^2 + 35x + 0`

- jim_thompson5910

do you see how ` -16x^2 + 35x + 0` matches up with `ax^2 + bx + c` ?

- anonymous

yes

- anonymous

so what do i plug in for x?

- jim_thompson5910

what are a,b,c equal to?

- anonymous

idk if i dont have the x values

- anonymous

do you want me to just do -16+35 cuz thats all we have

- jim_thompson5910

|dw:1443492881972:dw|

- jim_thompson5910

|dw:1443492905574:dw|

- jim_thompson5910

|dw:1443492921753:dw|

- jim_thompson5910

what are a,b,c equal to?

- anonymous

oh ok

- anonymous

-15

- anonymous

-15x2?

- anonymous

and 36x

- anonymous

and c?

- anonymous

so would it be -15x^2+36x+c?

- jim_thompson5910

a,b,c don't have any xs in them

- jim_thompson5910

a = -16
b = 35
c = 0
do you see how I'm getting this?

- jim_thompson5910

|dw:1443493159115:dw|

- anonymous

oh ok i was adding them

- anonymous

So would we plug in the max and min which would be 35 and 32 to the x's?

- anonymous

H(t) = -16(35/32)² + 35(35/32) = -19.141 which would be closest to D. Ok did i do it correctly?

- jim_thompson5910

are you familiar with the formula
h = -b/(2a)
??

- anonymous

yep

- jim_thompson5910

so you'll plug a = -16 and b = 35 into that formula to find h

- jim_thompson5910

tell me what h is

- jim_thompson5910

oh nvm, you already found h when you said 35/32

- jim_thompson5910

`H(t) = -16(35/32)² + 35(35/32) = -19.141` looks good

- jim_thompson5910

except that I get
-16(35/32)² + 35(35/32) = 19.140625

- jim_thompson5910

notice how the result is positive

- anonymous

yes I finally get how to do them now thank you.. i have a few more.

- anonymous

What is the domain of the following parabola?
A. All real numbers
B. x ≥ 1
C. x ≤ 2
D. y ≥ −3

- anonymous

##### 1 Attachment

- jim_thompson5910

tell me what you think

- anonymous

I think its all real numbers

- jim_thompson5910

why all real numbers?

- anonymous

i have no clue honestly i real don't know how to do it

- jim_thompson5910

so it was just a complete guess?

- anonymous

no I know that real numbers are both positve and negative so I thought it might be all real numbers

- jim_thompson5910

look at how the graph stretches infinitely to the left and right
compare the points on the parabola with the x axis

- anonymous

x=2

- anonymous

oh so C?? @jim_thompson5910

- jim_thompson5910

I think you're mixing up x and y

- jim_thompson5910

|dw:1443495131253:dw|

- jim_thompson5910

|dw:1443495141158:dw|

- jim_thompson5910

for each point, draw a vertical line until you hit the x axis
|dw:1443495166477:dw|

- jim_thompson5910

imagine you did this with EVERY point on the parabola. Which parts of the x axis would you be hitting?

- anonymous

Negative and positive

- anonymous

@jim_thompson5910 im confused

- jim_thompson5910

you will find that every point on the parabola will fill up the entire x axis

- jim_thompson5910

so that's why the answer is the set of all real numbers

- jim_thompson5910

we can plug in any real number for x and get some real number out for y

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