Using the graph at the left, it shows the height h in feet of a small rocket t seconds after it is launched. The path
of the rocket is given by the equation: h=-1612 + 128t
What is the maximum height of the rocket?

9514 1404 393

  256 feet

Step-by-step explanation:

The vertex of the quadratic ax^2 +bx +c is found at x=-b/(2a). This means the time at which the rocket reaches it maximum height is ...

  t = -128/(2(-16)) = 4 . . . . seconds

Evaluating h at t=4 gives the maximum height:

  h = -16(4^2) +128(4) = -256 +512 = 256

The maximum height of the rocket is 256 feet.

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If you can read this value from "the graph at the left," you can save yourself some computation.