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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

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rdacoder

Answer: B. (10, 50)

Step-by-step explanation:

y = 0.5(20x - [tex]x^{2}[/tex])

[tex]y=-\frac{1}{2} x^{2} + 10x[/tex]

to find x coord of vertex use the equation

[tex]\frac{-b}{2a}[/tex]

[tex]x=\frac{-10}{-1} \\\\x=10[/tex]

plug in x to the original equation

y = 0.5(20(10) - [tex](10)^{2}[/tex]

y = 0.5(100)

y = 50

Answer: (10, 50)

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