Question

A rocket's path is modeled by the equation y=−2x2+4x+6‍
. Graph the function. Identify the x-intercepts and interpret their meaning in the context of the rocket launch.(2 points)
x-intercepts (list smaller one first):
and
Using the context, interpret the meaning of the above x-intercept(s).(2 points)

Answer 1

x-intercepts (smaller first): -1 and 3

Interpretation: y = 0 means the rocket is on the ground. x = 3 is when (or where) the rocket returns to the ground (3 time/length units after launch). x = -1 is where the parabola crosses the ground before t = 0 (i.e., a time/place before the launch) and is not physically meaningful for the launch.

(For the graph: the parabola opens downward, has vertex at (1, 8) and axis of symmetry x = 1.)