Write an equation for a parabola.

Question

Write an equation for a parabola with a vertex at the origin, passing through (3,8), and symmetric with respect to the x-axis.

Answer 1

A parabola symmetric with the x-axis is a "sideways" parabola and its equation in vertex form is:

 

x = a(y-k)² + h

 

where (h,k) is the location of the vertex and is equal to (0,0) and a is a constant.  Hence:

 

x = a(y-0)² + 0 = ay²

 

To find a, plug in the value of the given point (3,8) and solve for a:

 

3 = a*8²

3 = a*64

3/64 = a

 

x = (3/64)y²