Quadratic equations word problem

Question

A tunnel is in the shape of a parabola. If the tunnel is 40 feet wide and has a maximum height of 12 feet. Write the equation of the quadratic function that represents the tunnel. (Let the axis of symmetry be the y-axis)

Answer 1

y = a(x-20)(x+20) in x intercept form. solve for a by plugging in the vertex point (0,12)

12 =a(-20)(20) = -400a

a = -12/400 = -3/100= -.03

y = -.03(x^2-400)

y =-.03x^2 +12 in vertex form