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

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.

graph them on a graphing calculator, press 2nd trace. select intersect. hit enter until it says answer. ti 84 works best

step-by-step explanation: