Question

if the equation given is y^2-6y=24x+3, how do i out this equation into standard form, using complete the square as needed?

Answer 1

why complete the square?

24x+3 = y^2-6y
24x = y^2-6y-3
x = 1/24 y^2 - 1/4 y - 1/8

That's standard form. To complete the square, you'd do

y^2-6y = 24x+3
y^2-6y+9 = 24x+3+9
(y-3)^2 = 24x+12
24x = (y-3)^2 - 12
x = 1/24 (y-3)^2 - 1/2

Looks like you need to review your text to get an idea of the mechanics involved.

This is also unusual, in that the axis of the parabola is horizontal, rather than vertical.