How do i find the vertex of a parabola given two points

Question

Hi i have been really stuck on my assignment for a while particularly this part where i need two  find the vertex of a parabola given two points

Answer 1

It isn't possible, because two points don't define a unique parabola. If all you are given is two points, and no other information, there are infinitely many parabolas that pass through those two points.

Answer 2

The equation of a parabola is a quadratic.

the form of a quadratic is :  y = ax² + bx + c 

the 3 unknowns are a, b, c.  

 

You need 3 pairs of x,y points to solve (which you can do with 3 independent linear equations formed with the 3 points).

 

2 points only define a line, which has 2 unknowns, a and b.  As in y = ax + b  

 

So unless there's other information you may inadvertently have left out, there are infinite parabolas through any 2 points.