SOLUTION: Use the given information about the polynomial graph to write the equation. Degree 3. Zeros at x = −2, x = 1, and x = 3. y-intercept at (0, −4).

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use the given information about the polynomial graph to write the equation. Degree 3. Zeros at x = −2, x = 1, and x = 3. y-intercept at (0, −4).      Log On


   

Question 1145560: Use the given information about the polynomial graph to write the equation.
Degree 3. Zeros at x = −2, x = 1, and x = 3.
y-intercept at (0, −4).
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
Given the zeros -2, 1 and 3, then
:
a * (x+2) * (x-1) * (x-3) = 0
:
a * (x^2 +x -2) * (x-3) = a * (x^3 -2x^2 -5x +6) = 0
:
y-intercept is (0, -4), substitute for x and y
:
-4 = a * ( 0^3 -2(0^2) -5(0) +6)
:
6a = -4
:
a = -4/6 = -2/3
:
f(x) = -2/3 * (x^3 -2x^2 -5x +6)
:
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f(x) = -2x^3 +4x^2/3 +10x/3 -4
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