Find the standard form of the equation of the parabola with the given characteristic(s)

Question

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin.

horizontal axis and passes through the point (7, −4)

Answer 1

Equation of parabola

y^2 =4ax

(-4^2) =4a(7)

16=28a

a= 16/28

a= 4/7

equation of parabola

y^2 = 4(4/7)x

y^2= 16x/7

7y^2= 16x.