Write an equation for a parabola with a vertex at the origin

Write an equation for a parabola with a vertex at the origin, passing through(6, 7), and symmetric with respect to the x-axis. An equation for this parabola is. (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Solution

Remember that the vertex form is: x = a(y - h)² + k with an axis along the x-axis.

Given: vertex at origin
Implied: You know that the origin is at (0, 0).
Means: h = 0
Means: k = 0

Plug in these values into the vertex form.
x = a(y - h)² + k
x = a(y - 0)² + 0
x = ay²

Given: point (6, 7)
Means: x = 6
Means: y = 7

Plug in these values into what you have and solve for a.
x = ay²
6= a(7)²
6 = a(49)
a=6/49


Update your equation.
x = ay²
x = (6/49)y²


ANSWER: x = (6/49)y²