Question

a physics class is planning an experiment about a toy rocket. the equation y = -16(x - 5.6)^2 + 502 gives the estimated height y, in feet, of the toy rocket x seconds after it is launched into the air. which of the following is the best interpretation of the vertex of the graph of the equation in the xy - plane? a this toy rocket reaches an estimated maximum height of 502 feet 16 seconds after it is launched into the air. b this toy rocket reaches an estimated maximum height of 502 feet 5.6 seconds after it is launched into the air. c this toy rocket reaches an estimated maximum height of 16 feet 502 seconds after it is launched into the air. d this toy rocket reaches an estimated maximum height of 5.6 feet 502 seconds after it is launched into the air.

Explanation:

The equation of the rocket's height is in vertex - form $y=a(x - h)^2 + k$, where $(h,k)$ is the vertex of the parabola. For a parabola opening downwards (since $a=-16<0$), the vertex represents the maximum point. Here, $h = 5.6$ and $k = 502$, meaning the maximum height $y = 502$ feet is reached at $x = 5.6$ seconds.

Answer:

B. This toy rocket reaches an estimated maximum height of 502 feet 5.6 seconds after it is launched into the air.