# How to find the equation of a parabola.

1. Apr 22, 2007

### john_blah

1. The problem statement, all variables and given/known data
Find the equation of the parabola if you have the following information:
Xintersects: (-4;0) and (0;0)
Yint: y = 7
Vertex: (-2;7)

2. Relevant equations
The equation must be in the standard form:
y=ax^2 + bx + c

3. The attempt at a solution
I know how to put it into the equation y = a(x^2 - p) + q but I have no idea how to put it into the y=ax^2 + bx + c form, which is asked.

Thanks

2. Apr 22, 2007

### cristo

Staff Emeritus
I think you mean you know how to put it in the form y = a(x - p)2 + q. Why not put it in this form and then expand the right hand side so it looks like y=ax2+bx+c?

3. Apr 22, 2007

### john_blah

Alright but unfortunately I have got no idea how to do that. Could you please elaborate?

4. Apr 22, 2007

### cristo

Staff Emeritus
Expand the right hand side to give y=a(x2-2px+p2)+q. Now can you spot the value of a,b and c in y=ax2+bx+c from this above expression?

5. Apr 22, 2007

### john_blah

Oh my word I cant believe I did not see that before!

Thank you! :rofl: