Question

Find an equation of the parabola with vertex (1, -1) that passes through the points (-1, 3) and (3, 3)

Answer 1

Welcome to Open Study. You are asked to find an equation of the parabola where you are given the vertex and a couple of points. First and foremost have you studies your text and know what a parabola equation looks like? there are two general equation forms, the standard and the vertex form. Do you know what they look like?

Answer 2

Here is a link, please refer to the link, if your study material does not enlighten you.

http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php

Answer 3

Yes I do know what parabolas look like

Answer 4

That was not my question, "Do you know what the "parabola equations" look like?

Answer 5

Yes I do. I am familiar with both forms.

Answer 6

O.K using the vertex form, what is "h" and "k" given to you for this parabola?

Answer 7

Hint. It is the x and y coordinates of the vertes.

Answer 8

(1, -1)

Answer 9

O.K very good, now substitute those values into the vertex form of the parabola equation. You should get something that looks like this;\[y = a(x-1)^{2}-1\]

Answer 10

Did you get that?

Answer 11

Yes I did!

Answer 12

Good. simplify by working it out getting \[y=a(x ^{2}-2x + 1) - 1\]\[y=ax ^{2}-2ax + a-1\]

Answer 13

Now we must solve for a. What was y when x=1, look at the vertex for the answer to that.

Answer 14

Y was -1

Answer 15

Use one of the points now and the equation and solve for a. Use the point (3,3) so if we mix up x and y it won't hurt.

3 = 9a - 6a + a -1
3 = 4a -1
4a = 4
a = 1

Did you follow that algebrta?

Answer 16

Yes I followed that

Answer 17

Note you can't us the vertex point to solve for a, as I was going to foolishly do as it was that point I used to develop the equation.

So the parabola equation is y = (x-1)^2 -1 in the vertex form or
y=x^2 - 2x

Answer 18

Thank you so much!

Answer 19

Good luck with your studies. You're welcome.