Question

The height h of a thrown object as a function of horizontal distance d that it has traveled is a quadratic function. An object is thrown from ground​ level, 57 m away from the base of a tower 17 m high and just barely clears the top of the tower. It then lands 57 m away on the other side. Find​ h(d), the quadratic function that represents this.

Answer 1

h(d) = (17/3249)(-d² +114d)

Explanation:

For this purpose, it is convenient to translate and scale a quadratic parent function so it has the desired characteristics. We can start with the function ...

f(x) = 1 -x² . . . . . . . has zeros at x = ±1 and a vertex at (0, 1)

We want to horizontally expand this function by a factor of 57, so we can replace x by x/57. We want to vertically scale it by a factor of 17, so the vertex is at (0, 17). Finally, we want to translate the function 57 m to the right, which requires replacing x with x-57. After these transformations, we have ...

f(x) = 17(1 -((x-57)/57)²) = (17/3249)(-x²+114x)

Using the appropriate function name and variable, we have ...

h(d) = (17/3249)(-d² +114d)