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Do you know what vertex form looks like?
isnt it y= a(x-h)^2 ? @q12157
y= a(x-h)^2+k where k is just any constant
luckily you dont have any constants in front of the x^2, so you can go straight into completing the square :p
Do you know how to complete the square?
no, but isnt it like factoring?
but 20 is k right?
sorta. basically the goal of completing the square is to get it into a (x-h)^2 state.
So in our problem y=x^2-12+20
what you do when you complete the square is you take the constant in front of x
-12 dont forget the negative sign
and then you divide it by 2 to get?
and then you square it to get?
so what you want to do now is you have your equation: y=x^2-12+20 and you want to add 36 and then subtract 36. This is so that you get: y=x^2-12+36+20-36 This is still the same equation as before right?
yep! and we end up with...... y= (x-6)^2+20? i think
y=x^2-12x+20 and y=x^2-12x+36+20-36 Sorry for the mistypes
close remember how we also subtracted a 36
so you need to do 20-36 as well
so what is your final answer?
oooo so y= (x-6)^2-16?
and that is in vertex form, so to answer your question from before, k=/=20 but instead -16
okay, i get it! can you help me with one more?
mhm sure lol
i know its like slope, but its a different formula i think
Oh this isnt so bad. I'm assuming average rate of change is constant from the two points.
Basically what you need to do is plug in those two points into the function g(x)
okay let me do that
so then you have two x points and two y points. Then you use the slope formula
So your two points should be?
15 and 33 are what i got when i plugged them in
and 3 is the y intercept i think so is that part of the points?
(4, 15) and (6, 33) yep!
oooo okay never mind that last thing
whenever you see rate of change, it just means slope. Rate of change = slope. So y intercept is unnecessary. Now you have your two points you can just find slope lol
is the rate of change 9? @q12157