Question

He

2
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Paula is standing on a bridge that is 110 above
the water below. She throws a pebble over
the edge of the bridge, and it hits the top of a
24 foot high bridge guard. The quadratic
equation that models the path of the pebble is:
p(t) = -16t² + 48t + 110
such that t is the time in seconds and p is
the height of the pebble.
What is the maximum height of the
pebble?
A) 2 feet
(B) 146 feet
C110 feet
D) 210 feet

Answer 1

(B) 146 feet

Explanation:

You want to know the maximum height of a pebble whose height is described by p(t) = -16t² + 48t + 110.

Vertex form

We can write the equation in vertex form as follows:

p(t) = -16(t² -3t) +110

p(t) = -16(t² -3t +2.25) +110 +16(2.25)

p(t) = -16(t -1.5)² +146

This shows the vertex of the quadratic curve to be (1.5, 146).

The maximum height of the pebble is 146 feet.