OpenStudy (maddisongruby):

can someone help me? i need like a walk through. im willing to do work, i just dont understand

2 years ago
OpenStudy (maddisongruby):

this is the problem

2 years ago
OpenStudy (anonymous):

Do you know what vertex form looks like?

2 years ago
OpenStudy (maddisongruby):

isnt it y= a(x-h)^2 ? @q12157

2 years ago
OpenStudy (anonymous):

y= a(x-h)^2+k where k is just any constant

2 years ago
OpenStudy (anonymous):

luckily you dont have any constants in front of the x^2, so you can go straight into completing the square :p

2 years ago
OpenStudy (anonymous):

Do you know how to complete the square?

2 years ago
OpenStudy (maddisongruby):

no, but isnt it like factoring?

2 years ago
OpenStudy (maddisongruby):

but 20 is k right?

2 years ago
OpenStudy (anonymous):

sorta. basically the goal of completing the square is to get it into a (x-h)^2 state.

2 years ago
OpenStudy (anonymous):

So in our problem y=x^2-12+20

2 years ago
OpenStudy (anonymous):

er y=x^2-12x+20

2 years ago
OpenStudy (anonymous):

what you do when you complete the square is you take the constant in front of x

2 years ago
OpenStudy (anonymous):

which is?

2 years ago
OpenStudy (maddisongruby):

12

2 years ago
OpenStudy (anonymous):

-12 dont forget the negative sign

2 years ago
OpenStudy (anonymous):

and then you divide it by 2 to get?

2 years ago
OpenStudy (maddisongruby):

6

2 years ago
OpenStudy (anonymous):

and then you square it to get?

2 years ago
OpenStudy (maddisongruby):

36

2 years ago
OpenStudy (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?

2 years ago
OpenStudy (maddisongruby):

yep! and we end up with...... y= (x-6)^2+20? i think

2 years ago
OpenStudy (anonymous):

y=x^2-12x+20 and y=x^2-12x+36+20-36 Sorry for the mistypes

2 years ago
OpenStudy (anonymous):

close remember how we also subtracted a 36

2 years ago
OpenStudy (anonymous):

so you need to do 20-36 as well

2 years ago
OpenStudy (anonymous):

so what is your final answer?

2 years ago
OpenStudy (maddisongruby):

oooo so y= (x-6)^2-16?

2 years ago
OpenStudy (anonymous):

Yep!!

2 years ago
OpenStudy (anonymous):

and that is in vertex form, so to answer your question from before, k=/=20 but instead -16

2 years ago
OpenStudy (maddisongruby):

okay, i get it! can you help me with one more?

2 years ago
OpenStudy (anonymous):

mhm sure lol

2 years ago
OpenStudy (maddisongruby):
2 years ago

OpenStudy (maddisongruby):

i know its like slope, but its a different formula i think

2 years ago
OpenStudy (anonymous):

Oh this isnt so bad. I'm assuming average rate of change is constant from the two points.

2 years ago
OpenStudy (anonymous):

Basically what you need to do is plug in those two points into the function g(x)

2 years ago
OpenStudy (maddisongruby):

okay let me do that

2 years ago
OpenStudy (anonymous):

so then you have two x points and two y points. Then you use the slope formula

2 years ago
OpenStudy (anonymous):

So your two points should be?

2 years ago
OpenStudy (maddisongruby):

15 and 33 are what i got when i plugged them in

2 years ago
OpenStudy (maddisongruby):

and 3 is the y intercept i think so is that part of the points?

2 years ago
OpenStudy (anonymous):

(4, 15) and (6, 33) yep!

2 years ago
OpenStudy (maddisongruby):

oooo okay never mind that last thing

2 years ago
OpenStudy (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

2 years ago
OpenStudy (maddisongruby):

so y2-y1/x2-x1?

2 years ago
OpenStudy (anonymous):

yep

2 years ago
OpenStudy (maddisongruby):

is the rate of change 9? @q12157

2 years ago
OpenStudy (anonymous):

yep!

2 years ago