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Complete the table for the function Y = x3 + 4x2 − 5x − 5.

Mathematics

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Here is the completed table for Y=x3+4x2−5x−5Y = x^3 + 4x^2 - 5x - 5:

  1. Calculate Y for X=−5X = -5.

    Y=(−5)3+4(−5)2−5(−5)−5=−125+4(25)+25−5=−125+100+25−5=−5Y = (-5)^3 + 4(-5)^2 - 5(-5) - 5 = -125 + 4(25) + 25 - 5 = -125 + 100 + 25 - 5 = -5
  2. Calculate Y for X=−4X = -4.

    Y=(−4)3+4(−4)2−5(−4)−5=−64+4(16)+20−5=−64+64+20−5=15Y = (-4)^3 + 4(-4)^2 - 5(-4) - 5 = -64 + 4(16) + 20 - 5 = -64 + 64 + 20 - 5 = 15
  3. Calculate Y for X=−2X = -2.

    Y=(−2)3+4(−2)2−5(−2)−5=−8+4(4)+10−5=−8+16+10−5=13Y = (-2)^3 + 4(-2)^2 - 5(-2) - 5 = -8 + 4(4) + 10 - 5 = -8 + 16 + 10 - 5 = 13
  4. Calculate Y for X=−1X = -1.

    Y=(−1)3+4(−1)2−5(−1)−5=−1+4(1)+5−5=−1+4+5−5=3Y = (-1)^3 + 4(-1)^2 - 5(-1) - 5 = -1 + 4(1) + 5 - 5 = -1 + 4 + 5 - 5 = 3
  5. Calculate Y for X=1X = 1.

    Y=(1)3+4(1)2−5(1)−5=1+4(1)−5−5=1+4−5−5=−5Y = (1)^3 + 4(1)^2 - 5(1) - 5 = 1 + 4(1) - 5 - 5 = 1 + 4 - 5 - 5 = -5
  6. Calculate Y for X=2X = 2.

    Y=(2)3+4(2)2−5(2)−5=8+4(4)−10−5=8+16−10−5=9Y = (2)^3 + 4(2)^2 - 5(2) - 5 = 8 + 4(4) - 10 - 5 = 8 + 16 - 10 - 5 = 9

    The completed table is:

    X−5−4−3−2−1012Y=x3+4x2−5x−5−51519133−5−59\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline X & -5 & -4 & -3 & -2 & -1 & 0 & 1 & 2 \\ \hline Y=x^3+4x^2-5x-5 & -5 & 15 & 19 & 13 & 3 & -5 & -5 & 9 \\ \hline \end{array}
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