The shape of the gateway arch in st louis, missouri, can be modeled by y=-0.0063x^2+4x, where x is the distance (in feet) from the left foot of the arch and y is the height ( in feet) of the arch above the graound. for what distances x is the arch more than 200 feet above the ground?

If y is our height in the function, in order to find where the x values where y = 200, we sub in accordingly: . In order to solve for these x values, we now have to factor this. Start by moving the 200 over to the other side by subtraction. Using the quadratic formula is the only way to do this easily. . Now we simplify a bit:

and a bit more

. We then have 2 solutions that are found in

and . Solving the first one gives us an x value of 57.72 feet, and solving the second one gives us an x value of 580.20 feet. Those are the x values where the arch is 200 feet above the ground. It will be on either side equally spaced from the vertex, which will be the highest point.

no, x cannot be the same number. in all of them, x is 1. for one input there is another output. g is not a function

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