An architectural engineer is designing a parabola dome that will be 200 feet in diameter with a max height of 50 feet. find the equation for the cross sectional parabola of the dome. y = what?

y = - 0.005x² + 50

Step-by-step explanation:

The diameter is 200 feet, so the parabola has roots at (-100, 0) and (100, 0). The maximum height is 50, so the vertex of the parabola is at (0, 50).

Using vertex form of a parabola:

y = a (x - h) ² + k

y = a (x - 0) ² + 50

y = ax² + 50

Plugging in either root:

0 = a (100) ² + 50

a = - 0.005

y = - 0.005x² + 50