Question 800849
Since your parabola has its turning point at the origin, (0,0), and focus on y axis the equation is
(1){{{ y = a*x^2 +0 +0 }}}
I include the two zeroes in the equations to indicate that the y-intercept is zero and the axis of symmetry is at x equals zero.
Since the parabola passes through the point (4,12) we have
(2) 12 = a*4^2 or
(3) 12 = 16a or
(4) a = 12/16 or
(5) a = 3/4
Let's check this.
Is (12 = 3/4*4^2)?
Is (12 = 3/4*16)?
Is (12 = 3*4)?
Is (12 = 12)? Yes
Answer: The equation of the parabola that meets the conditions stated is {{{y = (3/4)x^2}}}