Finding a parabola given two x intercepts

[revoz]

If you are given (5,0) and (-1,0) as the two x intercepts of a parabola is it possible to find the equation of the parabola? I have tried using the vertex formula for the x co-ordinate which is x = 2 the line of symmetry and plugging in either of these co-ordinates into y = ax^2 + bx + c but have too many unknowns to solve for. Is this unsolvable with only this information?

 

[symbolipoint]

This is possible only if you are looking for a general parabola; NOT for a specific one. In fact, you need THREE points to establish a specific parabola.

 

[Mentallic]

Only being given the roots of the parabola isn't sufficient enough to compile a specific parabola from it. There are an infinite number of parabolas having those 2 roots, all having different "steepness" and concavity.

e.g.

$$y=(x-5)(x+1)$$
$$y=2(5-x)(3x+3)$$

etc.

 

[revoz]

Thanks. I suppose if I tried different values for a and b I would come up with different parabolas. Wasn't sure if there was some way with the line of symmetry to determine the y value of the vertex but I realize that there are different options with only two points. Thanks again.