Answer:
- 3
- -2.25
- 3.0396
- 4
- -10197
Step-by-step explanation:
You want the quadratic expression evaluated for several different values of x.
Solution
Evaluating a polynomial is often easier when it is written in Horner form.
f(x) = -x² -2x +3
f(x) = (-x -2)x +3 = -(x +2)x +3
Repetitive evaluations are often easier to do by programming a spreadsheet or calculator to do them. The basic idea is to put the value where x is, then do the arithmetic.
1. f(0)
f(0) = -(0 +2)(0) +3 = 3
2. f(1.5)
f(1.5) = -(1.5 +2)(1.5) +3 = -(3.5)(1.5) +3 = -5.25 -3 = -2.25
3. f(-0.02)
f(-0.02) = -(-0.02 +2)(-0.02) +3 = (1.98)(0.02) +3 = 3.0396
4. f(-1)
f(-1) = -(-1 +2)(-1) +3 = 1 +3 = 4
5. f(100)
f(100) = -(100 +2)(100) +3 = -10200 +3 = -10197
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Additional comment
Horner form rewrites the polynomial to minimize the number of arithmetic operations required to evaluate it.
ax^5 +bx^4 +cx^3 +dx^2 +ex +f = ((((ax +b)x +c)x +d)x +e)x +f
