Evaluating Polynomial Functions
The formula D = -16t2 + v0t + s0 is used to model the effect of gravity on an object
tossed straight upward with initial velocity v0 feet per second from an initial
height of s0 feet. Because D is determined by t, we say
that D is a function of t. The values of t range from t = 0 when the ball is tossed to
the time when it hits the ground. To emphasize that the value of D depends on t, we
can use the function notation and write
D(t) = -16t 64t + 4.
We read D(t) as “D of t.†The expression D(t) is the value of the polynomial at
time t. To find the value when t = 2, replace t by 2:
| D(2) |
= -16 · 22 + 64 · 2 + 4 = -16 ·
4 + 128 + 4
= 68 |
The statement D(2) = 68 means that the ball is 68 feet above the ground 2 seconds
after the ball was tossed upward. Note that D(2) does not mean D times 2.
Example 1
Finding the value of a polynomial
Suppose Q(x) = 2x3 - 3x2 - 7x - 6. Find Q(3) and Q(-1).
Solution
To find Q(3), replace x by 3 in Q(x) = 2x3 - 3x2 - 7x - 6:
| Q(3) |
= 2 · 33 - 3 · 32 - 7 ·
3 - 6 = 54 - 27 - 21 - 6
= 0 |
To find Q(-1), replace x by -1 in Q(x) = 2x3 - 3x2 - 7x
- 6:
| Q(-1) |
= 2(-1)3 - 3(-1)2 - 7(-1) - 6 = -2
- 3 + 7 - 6
= -4 |
So Q(3) = 0 and Q(-1) = -4.
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