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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)?
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?
post one at a time please
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
its positive so...
yes, the x-h matches up with x-3 h = 3
ohh ok i got it
it wouldn't be -3 tho?
no, think of it as like the opposite h-3 ----> shift 3 units to the RIGHT
here are the choices... the answer would be B then right?
Left 3 units Right 3 units Up 3 units Down 3 units
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
oh so would the answer be B or A? @jim_thompson5910
like I said and drew, f shifts 3 units to the right
Oh thank you!
For the second, here are the choices
17.9 feet 18.2 feet 18.7 feet 19.1 feet
`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?
s is 0?
v is 35
yes on both
so `H(t) = -16t^2 + vt + s` turns into `H(t) = -16t^2 + 35t + 0` which is really `H(t) = -16t^2 + 35t`
how do i solve without t though?
I'm going to replace every t in ` -16t^2 + 35t + 0` with x so we have ` -16x^2 + 35x + 0`
do you see how ` -16x^2 + 35x + 0` matches up with `ax^2 + bx + c` ?
so what do i plug in for x?
what are a,b,c equal to?
idk if i dont have the x values
do you want me to just do -16+35 cuz thats all we have
what are a,b,c equal to?
so would it be -15x^2+36x+c?
a,b,c don't have any xs in them
a = -16 b = 35 c = 0 do you see how I'm getting this?
oh ok i was adding them
So would we plug in the max and min which would be 35 and 32 to the x's?
H(t) = -16(35/32)² + 35(35/32) = -19.141 which would be closest to D. Ok did i do it correctly?
are you familiar with the formula h = -b/(2a) ??
so you'll plug a = -16 and b = 35 into that formula to find h
tell me what h is
oh nvm, you already found h when you said 35/32
`H(t) = -16(35/32)² + 35(35/32) = -19.141` looks good
except that I get -16(35/32)² + 35(35/32) = 19.140625
notice how the result is positive
yes I finally get how to do them now thank you.. i have a few more.
What is the domain of the following parabola? A. All real numbers B. x ≥ 1 C. x ≤ 2 D. y ≥ −3
tell me what you think
I think its all real numbers
why all real numbers?
i have no clue honestly i real don't know how to do it
so it was just a complete guess?
no I know that real numbers are both positve and negative so I thought it might be all real numbers
look at how the graph stretches infinitely to the left and right compare the points on the parabola with the x axis
oh so C?? @jim_thompson5910
I think you're mixing up x and y
for each point, draw a vertical line until you hit the x axis |dw:1443495166477:dw|
imagine you did this with EVERY point on the parabola. Which parts of the x axis would you be hitting?
Negative and positive
@jim_thompson5910 im confused
you will find that every point on the parabola will fill up the entire x axis
so that's why the answer is the set of all real numbers
we can plug in any real number for x and get some real number out for y