# Finding a parabola given two x intercepts

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?

Related Precalculus Mathematics Homework Help News on Phys.org
symbolipoint
Homework Helper
Gold Member
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
Homework Helper
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.

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.