How to find the equation of a parabola.

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Homework Help Overview

The discussion revolves around finding the equation of a parabola given specific points: x-intercepts, y-intercept, and vertex. The subject area is algebra, specifically focusing on quadratic functions and their standard forms.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the transition from a vertex form of the equation to the standard form. There is an exploration of how to expand the vertex form to identify coefficients a, b, and c.

Discussion Status

Some participants have provided guidance on how to expand the vertex form to reach the standard form. There is an acknowledgment of initial confusion, but a productive direction has been established through collaborative questioning and elaboration.

Contextual Notes

The original poster expresses uncertainty about the transformation process required to convert the vertex form into the standard form as specified in the homework requirements.

john_blah
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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
 
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john_blah said:

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?
 
Alright but unfortunately I have got no idea how to do that. Could you please elaborate?
 
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?
 
Oh my word I can't believe I did not see that before!

Thank you! :smile:
 

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