Question

A rock is launched from a cannon. Its height, h(x), can be represented by a

quadratic function in terms of time, x, in
seconds.

After 1 second, the rock is 94 feet in the
air; after 2 seconds, it is 176 feet in the
air.

Complete the height function, h(x), for this situation

h(x) =

Answer 1

To complete the height function for the rock that is launched from a cannon, we need to find the equation for the quadratic function. Given the height of the rock at two different times, we can form two equations and solve them to determine the coefficients of the quadratic function. This will allow us to complete the height function for the situation.

Step-by-step explanation:

To complete the height function for the rock that is launched from a cannon, we need to find the equation for the quadratic function.

Let's assume the height function, h(x), is of the form h(x) = ax^2 + bx + c.

Given that after 1 second the rock is 94 feet in the air and after 2 seconds it is 176 feet in the air, we can substitute these values into the equation to form two equations:

1. h(1) = a(1)^2 + b(1) + c = 94
2. h(2) = a(2)^2 + b(2) + c = 176

Solving these two equations will give us the values of a, b, and c, and thereby complete the height function, h(x).