Question

The height is modeled by h(x) = -0.03x² + x + 48, where h(x) is the height in feet, of the stream of water x feet from the fire truck.

What is the maximum height the water from this nozzle can reach? What is the maximum distance from the firetruck a firefighter can stand and still reach the fire?
A) Maximum height: 48 feet, Maximum distance: 50 feet
B) Maximum height: 48 feet, Maximum distance: 33.33 feet
C) Maximum height: 50 feet, Maximum distance: 48 feet
D) Maximum height: 33.33 feet, Maximum distance: 48 feet

Answer 1

The maximum height the water from the nozzle can reach is 48 feet, and the maximum distance from the firetruck a firefighter can stand and still reach the fire is 50 feet.

Step-by-step explanation:

To find the maximum height the water from the nozzle can reach, we need to find the vertex of the quadratic function h(x) = -0.03x² + x + 48. The vertex of a quadratic function in the form y = ax² + bx + c is given by the coordinates (-b/2a, f(-b/2a)), where a, b, and c are the coefficients of the quadratic function.

In this case, a = -0.03, b = 1, and c = 48. Plugging these values into the formula, we get (-1/2*(-0.03), h(-1/2*(-0.03))). Simplifying further, we find the maximum height is 48 feet.

The maximum distance from the firetruck a firefighter can stand and still reach the fire is equal to the horizontal distance from the firetruck to the x-coordinate of the vertex. This can be found using the formula -b/2a. Plugging in the values, we get -1/2*(-0.03) = 50. Hence, the maximum distance is 50 feet.