The function f(x)=−0.0025x2+0.243x+3 models the path of a rocket in feet. Explain how you would use the function to determine the height the rocket was launched from, how far it traveled, and the greatest height it reached. Answer in complete sentences.

The quadratic function models the path of the rocket. When we substitute an x value, we can determine the height in feet of the rocket.

To determine the height it was launched from, we would look at the y-intercept. This represents the starting value, as time = 0 in this point (cannot have negative time).

To determine how far the rocket traveled, we would look at the positive x-intercept of the expression. At this point, height = 0, so we can see the distance from start to finish of the rocket.

To determine the greatest height achieve, we would look at the vertex of the parabola generated from the given function. Using (-b/a, f(-b/a)), we can determine the greatest height achieved.