Question

y=a(x-h)^2+k what do the letters represent and do?

Answer 1

(h,k) is the vertex
(x,y) is any point on the parabola

a is the vertical stretch/compression factor

Answer 2

does h determine if it is a positive or negative parabola?

Answer 3

If a is positive, then the parabola opens up.
If a is negative, then the parabola opens down.

Answer 4

i'm sorry but what is the job of h and k then ? i know itz the vertex just a little confused ..

Answer 5

(h , k) is just the vertex. The vertex is just the peak or valley of the graph of a parabola. The equation is written in vertex form to make it convenient to identify where the vertex is on the parabola. I don't really know what more you need about it.

Answer 6

mmm... ok thank-you :) i'll try my best from the information given :D

Answer 7

Well, maybe this is what you need:

The parent graph is \(y = x^2\).
\(h\) shifts \(x^2\) horizontally h units to the right
\(k\) shifts \(x^2\) vertically h units upwards.

You end up with

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

And of course (h,k) together represent the vertex.

Answer 8

Well the above assumes that \(a = 1\) . If \(a\) is something other than 1, then the graph will be different of course.

Answer 9

You have more than enough information to understand this I believe.

Answer 10

perfect! now i understand thank-you so much!

Answer 11

Well, I'm going to re-write the above. If you don't have \(h\) or \(k\) , then you just have

\(y = ax^2\)

And then \(h\) shifts the graph horizontally left or right depending on the value of h
\(k\) shifts the graph vertically up or down depending on its value.

After the shifting is finished, you have

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

Answer 12

got it thanks! (:

Answer 13

When I said "you don't have \(h\) or \(k\) I meant that \((h,k) = (0,0)\). Every parabola must have an \(h\) and \(k\) value. Even if their values are both zero.

Answer 14

ohh ok! so when grahing it would strat at (0,0) and in the equation i dont really have to include it correct?

Answer 15

When you are graphing a parabola you should start with the vertex if you know what the vertex is.

If you have \(y = 5x^2\) obviously the vertex is (0,0)

If you have \(y = 5(x - 4)^2 + 7\) then the vertex is (4,7) and you would start with (4,7) not (0,0)

Answer 16

it's fine if u dont know but imma ask maybe u will understand. if the parabola is not a function but it is a "sleeping" porabula will it be the same equation?

Answer 17

I know what the question is asking. The graph will not be the same.

Answer 18

so itz a different equation since itz no longer the same?

Answer 19

It has to be different since its graph has changed. Every graph has a unique equation associated with it.

Answer 20

alrighty thanks