Question

IM GIVING MEDALS TO SOMEONE WHO ANSWERS THIS! Will someone write the function for when the vertex of a parabola is at (2,3) and passes through the points (1,2) and (1,4) thanks(:

Answer 1

@phi @hero @mathstudent55

Answer 2

You have three points, thus you have three formulas.
\[3=a2^{2}+b(2)+c \]
\[2=a1^{2}+b(1)+c\]
\[4=a1^{2}+b(1)+c\]

Answer 3

@hlambach It just shows a graph and I need to know the function of it to compare it to my other functions. It's supposed to equal h(x). I probably should have included that

Answer 4

This is terrible quality but here is a pic

Answer 5

Please help ): @hlambach

Answer 6

@igreen

Answer 7

Sorry, my internet is really slow right now.

Answer 8

So it gives you the points?

Answer 9

You can right it in vertex form and then FOIL.
Vertex form is \[y=a(x-h)^{2}+k\]
(-h,k) is your vertex. The vertex in the graph is (3,2)
Substitute it in.

Answer 10

@hlambach thank you omg hang on

Answer 11

*write

Answer 12

haha, no proble.

Answer 13

@hlambach so h(x)=a(x-3)^2=2?

Answer 14

The formula is a(x-3)^2=2. FOIL that. So multiply it out.

Answer 15

Take the = 2 off the end I have no idea why I put that

Answer 16

Thanks for the medal. :)

Answer 17

I'm so sorry, wait. Before you multiply it out. You need to find a. To find a, use any point on the graph (that isn't the vertex) and put it in for x and y.

Answer 18

@hlambach it's okay haha thank you so much I've been stuck on this forever

Answer 19

So solve for a in this equation
(1,2)
2=a(1-3)^2+2. (sorry, I forgot to add the +2 on the previous equation.)

Answer 20

Once you get that, change the equation back to
y=(whatever you get for a)(x-3)^2+2
and multiply it all out.

Answer 21

Once that's done just change the y to h(x). (It's the same thing.

Answer 22

Get it? @Kaitlynbrooks33

Answer 23

@hlambach Yes thank you(: is there anyway to give multiple medals lol

Answer 24

haha, I wish there were. Glad I could help! Make sure to close the question!