Question

@phi Can you please help me with this test?!? I have only need help with one thing.

Answer 1

Can you please help me get the h(x) graph into a equation?

Answer 2

Do you know the "vertex form" of the equation for a parabola?

Answer 3

y=a(x-h)^2+k

(h,k) is the vertex

Answer 4

what is the vertex for your parabola ?

Answer 5

1,3

Answer 6

are you sure the the vertex is at 1,3 ?

Answer 7

I think so I really can't see, thats part of my problem the graphs are too small.

Answer 8

Here is where the point (1,3) is on your graph

Answer 9

oh duh.... so -1,-3

Answer 10

(although I am sure the vertex is NOT -1,-3)

Answer 11

You fixed the y value and made the x value wrong.

Answer 12

Here is where (-1,-3) is

Answer 13

1,-3

Answer 14

Now (finally!)
Replace h and k in your equation with those numbers.
after you do that, what do you have ?

Answer 15

h(x)=a (x-1)^2-3

Answer 16

next step is to find "a"

to do that, find a "nice" spot on the graph where you can read off the x and y values.
Can you find a point where the graph goes exactly through where the lines cross, and then read the what point that is ?

Answer 17

0,-1

Answer 18

now replace h(x) with -1 and x with 0 in your equation. what do you get ?

Answer 19

-1=(0-1)^2-3 ?

Answer 20

what happened to the "a" ?

Answer 21

so its h(x)=-1(0-1)^2-3

Answer 22

No. you start with
h(x)=a (x-1)^2-3

which by the way is the same as
y = a (x-1)^2 -3

replace x with 0 and y with -1 (because (0,-1) is on the parabola)
you leave the "a" alone.

try again

Answer 23

-1=a(0-1)^2-3

Answer 24

can you simplify that?

Answer 25

remember PEDMAS parentheses, exponents, divide/multiply, add/subtract
is the order of operations.

Answer 26

inside the parens you have (0-1) what does that simplify to ?

Answer 27

2

Answer 28

are you saying that 0 - 1 is 2 ?

Answer 29

simplifying the whole thing is 2 i think

Answer 30

-1= a(0-1)^2 - 3

0-1 is -1

\[ -1 = a(-1)^2 - 3 \]
-1*-1 is 1 and a*1 is a
\[ -1 = a - 3 \]
add +3 to both sides
\[ 3-1= a -3 + 3 \\2=a\]

Answer 31

that is the last missing piece in your equation.

Answer 32

so h(x)=2(x-1)^2-3

Answer 33

yes, that looks good.

Answer 34

Thank you!!

Answer 35

yw