A parabola has a vertex at (0,0); a horizontal axis; and the point (12,6) is on the parabola. Write the equation of the parabola in standard form.

the equation must of the form

x = ay^2
sub in the point (12,6) to find a

x^2=9/144y

To write the equation of a parabola in standard form, you need to use the general equation for a parabola with a horizontal axis of symmetry. The standard form of a parabola with the vertex (h, k) is given by:

(x – h)^2 = 4p(y – k)

where "p" is the distance between the vertex and the focus/directrix. Since the vertex of the given parabola is at (0,0) and it has a horizontal axis of symmetry, the equation becomes:

x^2 = 4p(y – 0)

Simplifying further, we have:

x^2 = 4py

Now, we need to determine the value of "p" using the information that the point (12,6) lies on the parabola.

Substitute the coordinates (x = 12, y = 6) into the equation:

(12)^2 = 4p(6)

144 = 24p

Now, solve for "p" by dividing both sides of the equation by 24:

p = 144/24
p = 6

Finally, substitute the value of "p" back into the equation:

x^2 = 4(6)y

Simplifying further:

x^2 = 24y

Therefore, the equation of the given parabola in standard form is x^2 = 24y.