Question

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

Answer 1

this is the problem

Answer 2

Do you know what vertex form looks like?

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

Do you know how to complete the square?

Answer 7

no, but isnt it like factoring?

Answer 8

but 20 is k right?

Answer 9

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

Answer 10

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

Answer 11

er y=x^2-12x+20

Answer 12

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

Answer 13

which is?

Answer 14

12

Answer 15

-12 dont forget the negative sign

Answer 16

and then you divide it by 2
to get?

Answer 17

6

Answer 18

and then you square it to get?

Answer 19

36

Answer 20

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?

Answer 21

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

Answer 22

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

Answer 23

close remember how we also subtracted a 36

Answer 24

so you need to do 20-36 as well

Answer 25

so what is your final answer?

Answer 26

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

Answer 27

Yep!!

Answer 28

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

Answer 29

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

Answer 30

mhm sure lol

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

okay let me do that

Answer 35

so then you have two x points and two y points.

Then you use the slope formula

Answer 36

So your two points should be?

Answer 37

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

Answer 38

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

Answer 39

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

Answer 40

oooo okay never mind that last thing

Answer 41

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

Answer 42

so y2-y1/x2-x1?

Answer 43

yep

Answer 44

is the rate of change 9? @q12157

Answer 45

yep!