Question

The flight path of a rocket, launched from the ground, is modeled by y = 0.5(20x – x2), where y is the height of the rocket in feet from the ground and x is the time in seconds after it was launched. Find the vertex of the parabola and explain what it represents in terms of the context.

a. (20, 0); rocket lands at 0 feet after 20 seconds
b. (10, 50); rocket reaches maximum height of 50 feet after 10 seconds
c. (10, 50); rocket reaches maximum height of 10 feet after 50 seconds
d. (20, 0); rocket reaches 20 feet after 0 seconds

Answer 1

(10, 50); rocket reaches maximum height of 50 feet after 10 seconds

Explanation:

After 10 seconds (x) the rocket reaches a height of 50ft (y)

Answer 2

Answer: B. (10, 50)

Explanation:

y = 0.5(20x -
`x^(2)`)

`y=-(1)/(2) x^(2) + 10x`

to find x coord of vertex use the equation

`(-b)/(2a)`

`x=(-10)/(-1) \\\\x=10`

plug in x to the original equation

y = 0.5(20(10) -
`(10)^(2)`

y = 0.5(100)

y = 50

Answer: (10, 50)