maddisonGruby
  • maddisonGruby
can someone help me? i need like a walk through. im willing to do work, i just dont understand
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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maddisonGruby
  • maddisonGruby
this is the problem
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anonymous
  • anonymous
Do you know what vertex form looks like?
maddisonGruby
  • maddisonGruby
isnt it y= a(x-h)^2 ? @q12157

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anonymous
  • anonymous
y= a(x-h)^2+k where k is just any constant
anonymous
  • anonymous
luckily you dont have any constants in front of the x^2, so you can go straight into completing the square :p
anonymous
  • anonymous
Do you know how to complete the square?
maddisonGruby
  • maddisonGruby
no, but isnt it like factoring?
maddisonGruby
  • maddisonGruby
but 20 is k right?
anonymous
  • anonymous
sorta. basically the goal of completing the square is to get it into a (x-h)^2 state.
anonymous
  • anonymous
So in our problem y=x^2-12+20
anonymous
  • anonymous
er y=x^2-12x+20
anonymous
  • anonymous
what you do when you complete the square is you take the constant in front of x
anonymous
  • anonymous
which is?
maddisonGruby
  • maddisonGruby
12
anonymous
  • anonymous
-12 dont forget the negative sign
anonymous
  • anonymous
and then you divide it by 2 to get?
maddisonGruby
  • maddisonGruby
6
anonymous
  • anonymous
and then you square it to get?
maddisonGruby
  • maddisonGruby
36
anonymous
  • anonymous
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?
maddisonGruby
  • maddisonGruby
yep! and we end up with...... y= (x-6)^2+20? i think
anonymous
  • anonymous
y=x^2-12x+20 and y=x^2-12x+36+20-36 Sorry for the mistypes
anonymous
  • anonymous
close remember how we also subtracted a 36
anonymous
  • anonymous
so you need to do 20-36 as well
anonymous
  • anonymous
so what is your final answer?
maddisonGruby
  • maddisonGruby
oooo so y= (x-6)^2-16?
anonymous
  • anonymous
Yep!!
anonymous
  • anonymous
and that is in vertex form, so to answer your question from before, k=/=20 but instead -16
maddisonGruby
  • maddisonGruby
okay, i get it! can you help me with one more?
anonymous
  • anonymous
mhm sure lol
maddisonGruby
  • maddisonGruby
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maddisonGruby
  • maddisonGruby
i know its like slope, but its a different formula i think
anonymous
  • anonymous
Oh this isnt so bad. I'm assuming average rate of change is constant from the two points.
anonymous
  • anonymous
Basically what you need to do is plug in those two points into the function g(x)
maddisonGruby
  • maddisonGruby
okay let me do that
anonymous
  • anonymous
so then you have two x points and two y points. Then you use the slope formula
anonymous
  • anonymous
So your two points should be?
maddisonGruby
  • maddisonGruby
15 and 33 are what i got when i plugged them in
maddisonGruby
  • maddisonGruby
and 3 is the y intercept i think so is that part of the points?
anonymous
  • anonymous
(4, 15) and (6, 33) yep!
maddisonGruby
  • maddisonGruby
oooo okay never mind that last thing
anonymous
  • anonymous
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
maddisonGruby
  • maddisonGruby
so y2-y1/x2-x1?
anonymous
  • anonymous
yep
maddisonGruby
  • maddisonGruby
is the rate of change 9? @q12157
anonymous
  • anonymous
yep!

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