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:

Step1: Recall vertex - form of quadratic function

The vertex - form of a quadratic function is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola. For the given function $y=-16(x - 5.6)^2+502$, we have $a=-16$, $h = 5.6$, and $k = 502$.

Step2: Analyze the meaning of vertex

Since $a=-16<0$, the parabola opens downwards, and the vertex $(h,k)=(5.6,502)$ represents the maximum point of the function. Here, $x$ represents the time in seconds after the rocket is launched and $y$ represents the height in feet. So, at $x = 5.6$ seconds, the height $y$ reaches its maximum value of 502 feet.

Answer:

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