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