find the equation of the parabola:

Question

through the point (-5/3,4) with vertex (0,0)

Answer 1

Consider the vertex form (some books refer to it as standard form) of the parabolic equation: y-k = a(x-h)²

where (h,k) is the vertex of the parabola, and a is a constant. This is assuming that the parabola is vertical, not horizontal. In fact, either case could be true and still meet the conditions as stated. But we will assume vertical for this explanation.

 

Given that the vertex is (0,0), the vertex equation becomes y = ax²

 

We then use the other given point (-5/3,4) as x and y to solve for a.

 

4 = a(-5/3)² so a = 4/(25/9)=4(9/25)=36/25

 

This yields the equation:  y = (36/25)x²