How to find the equation of a parabola.

[john_blah]

Homework Statement

Find the equation of the parabola if you have the following information:
Xintersects: (-4;0) and (0;0)
Yint: y = 7
Vertex: (-2;7)

Homework Equations

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

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

 

[cristo]

Homework Statement

Find the equation of the parabola if you have the following information:
Xintersects: (-4;0) and (0;0)
Yint: y = 7
Vertex: (-2;7)

Homework Equations

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

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

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?

 

[john_blah]

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

 

[cristo]

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?

 

[john_blah]

Oh my word I can't believe I did not see that before!

Thank you!