To find the equation of a parabola, substitute the vertex coordinates for h and k, substitute the coordinates of another point on the parabola for x and y and then solve for a. The equations will differ depending on whether the parabola is vertical or horizontal.
The equation for a vertical parabola is y=a(x-h)2+k and the equation for a horizontal is x=a(y-k)2+h. The steps to solve the equation remain the same.
Step 1: Use the right formula and plug in the numbers
Determine whether the parabola is vertical or horizontal. Substitute the coordinates for the vertex into h and k in the formula. Choose a point on the figure, other than the vertex, and substitute those coordinates into x and y in the formula.
Step 2: Solve for the value of a
Once all of the numbers have been plugged in, use simple algebra to solve for the value of a in the formula.
Step 3: Rewrite the formula
Rewrite the formula using the vertex coordinates for the values of h and k, and the value for a that was obtained from the calculation in Step 2. The final answer will resemble an algebra problem, with unknowns represented by x and y. An example of an equation for a vertical parabola is y=2(x-5)2+3.