anonymous
  • anonymous
Does anyone want to help me with math for a fan and medal?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@jim_thompson5910
anonymous
  • 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
  • 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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jim_thompson5910
  • jim_thompson5910
post one at a time please
anonymous
  • anonymous
sorry
jim_thompson5910
  • 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
  • anonymous
its positive so...
jim_thompson5910
  • jim_thompson5910
yes, the x-h matches up with x-3 h = 3
anonymous
  • anonymous
ohh ok i got it
anonymous
  • anonymous
it wouldn't be -3 tho?
anonymous
  • anonymous
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
no, think of it as like the opposite h-3 ----> shift 3 units to the RIGHT
jim_thompson5910
  • jim_thompson5910
|dw:1443491690709:dw|
anonymous
  • anonymous
ohhhh ok!
jim_thompson5910
  • jim_thompson5910
|dw:1443491701434:dw|
anonymous
  • anonymous
here are the choices... the answer would be B then right?
anonymous
  • anonymous
Left 3 units Right 3 units Up 3 units Down 3 units
jim_thompson5910
  • 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
  • anonymous
oh so would the answer be B or A? @jim_thompson5910
jim_thompson5910
  • jim_thompson5910
like I said and drew, f shifts 3 units to the right
anonymous
  • anonymous
Oh thank you!
anonymous
  • anonymous
For the second, here are the choices
anonymous
  • anonymous
17.9 feet 18.2 feet 18.7 feet 19.1 feet
jim_thompson5910
  • 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
  • anonymous
s is 0?
anonymous
  • anonymous
v is 35
anonymous
  • anonymous
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
yes on both
jim_thompson5910
  • 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
  • anonymous
how do i solve without t though?
jim_thompson5910
  • 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
  • jim_thompson5910
do you see how ` -16x^2 + 35x + 0` matches up with `ax^2 + bx + c` ?
anonymous
  • anonymous
yes
anonymous
  • anonymous
so what do i plug in for x?
jim_thompson5910
  • jim_thompson5910
what are a,b,c equal to?
anonymous
  • anonymous
idk if i dont have the x values
anonymous
  • anonymous
do you want me to just do -16+35 cuz thats all we have
jim_thompson5910
  • jim_thompson5910
|dw:1443492881972:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1443492905574:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1443492921753:dw|
jim_thompson5910
  • jim_thompson5910
what are a,b,c equal to?
anonymous
  • anonymous
oh ok
anonymous
  • anonymous
-15
anonymous
  • anonymous
-15x2?
anonymous
  • anonymous
and 36x
anonymous
  • anonymous
and c?
anonymous
  • anonymous
so would it be -15x^2+36x+c?
jim_thompson5910
  • jim_thompson5910
a,b,c don't have any xs in them
jim_thompson5910
  • jim_thompson5910
a = -16 b = 35 c = 0 do you see how I'm getting this?
jim_thompson5910
  • jim_thompson5910
|dw:1443493159115:dw|
anonymous
  • anonymous
oh ok i was adding them
anonymous
  • anonymous
So would we plug in the max and min which would be 35 and 32 to the x's?
anonymous
  • 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
  • jim_thompson5910
are you familiar with the formula h = -b/(2a) ??
anonymous
  • anonymous
yep
jim_thompson5910
  • jim_thompson5910
so you'll plug a = -16 and b = 35 into that formula to find h
jim_thompson5910
  • jim_thompson5910
tell me what h is
jim_thompson5910
  • jim_thompson5910
oh nvm, you already found h when you said 35/32
jim_thompson5910
  • jim_thompson5910
`H(t) = -16(35/32)² + 35(35/32) = -19.141` looks good
jim_thompson5910
  • jim_thompson5910
except that I get -16(35/32)² + 35(35/32) = 19.140625
jim_thompson5910
  • jim_thompson5910
notice how the result is positive
anonymous
  • anonymous
yes I finally get how to do them now thank you.. i have a few more.
anonymous
  • anonymous
What is the domain of the following parabola? A. All real numbers B. x ≥ 1 C. x ≤ 2 D. y ≥ −3
anonymous
  • anonymous
jim_thompson5910
  • jim_thompson5910
tell me what you think
anonymous
  • anonymous
I think its all real numbers
jim_thompson5910
  • jim_thompson5910
why all real numbers?
anonymous
  • anonymous
i have no clue honestly i real don't know how to do it
jim_thompson5910
  • jim_thompson5910
so it was just a complete guess?
anonymous
  • anonymous
no I know that real numbers are both positve and negative so I thought it might be all real numbers
jim_thompson5910
  • 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
  • anonymous
x=2
anonymous
  • anonymous
oh so C?? @jim_thompson5910
jim_thompson5910
  • jim_thompson5910
I think you're mixing up x and y
jim_thompson5910
  • jim_thompson5910
|dw:1443495131253:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1443495141158:dw|
jim_thompson5910
  • jim_thompson5910
for each point, draw a vertical line until you hit the x axis |dw:1443495166477:dw|