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9. RATIONAL NUMBERS, REAL NUMBERS, AND ALGEBRA
Graphs of Quadratic Functions
Example. A ball is tossed up vertically at a velocity of 72 feet per second
from a point 10 feet above the ground. It is known from physics that the height
of the ball above the ground, in feet, is given by the position function
p(t) =
16t2 + 72t + 10,
where t is the time in seconds. At what time t is the ball at its highest point?
solution.
A quadratic function is a function of the form f (x) = ax2 + bx + c where a, b,
and c are constants and a 6= 0. Graphs of quadratic functions are parabolas.
Our function p is a quadratic function. We form a table of values and its graph.
t (sec) 0 1 2 3 4
p(t) (ft) 10 66 90 82 42
We plot our points and draw a smooth curve through them. The ball is at its
highest point between 2 and 3 seconds.