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Complete the table for the relation y = x2 − 4x − 21 for x values from -4 to 8.

Mathematics

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Graph of y = x² − 4x − 21

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Key points of y = x² − 4x − 21
Pointxy
x-intercept−30
y-intercept0−21
Minimum2−25
x-intercept70

Step-by-step solution

3 steps

  1. Understand the relation and the given table.

    The relation is y=x2−4x−21y = x^2 - 4x - 21. We need to complete the table for xx values from −4-4 to 8.

  2. Calculate the missing yy values using the given relation.

    • For x=−2x = -2: y=(−2)2−4(−2)−21=4+8−21=12−21=−9y = (-2)^2 - 4(-2) - 21 = 4 + 8 - 21 = 12 - 21 = -9

    • For x=−1x = -1: y=(−1)2−4(−1)−21=1+4−21=5−21=−16y = (-1)^2 - 4(-1) - 21 = 1 + 4 - 21 = 5 - 21 = -16

    • For x=2x = 2: y=(2)2−4(2)−21=4−8−21=−4−21=−25y = (2)^2 - 4(2) - 21 = 4 - 8 - 21 = -4 - 21 = -25

    • For x=3x = 3: y=(3)2−4(3)−21=9−12−21=−3−21=−24y = (3)^2 - 4(3) - 21 = 9 - 12 - 21 = -3 - 21 = -24

    • For x=5x = 5: y=(5)2−4(5)−21=25−20−21=5−21=−16y = (5)^2 - 4(5) - 21 = 25 - 20 - 21 = 5 - 21 = -16

    • For x=6x = 6: y=(6)2−4(6)−21=36−24−21=12−21=−9y = (6)^2 - 4(6) - 21 = 36 - 24 - 21 = 12 - 21 = -9

    • For x=7x = 7: y=(7)2−4(7)−21=49−28−21=21−21=0y = (7)^2 - 4(7) - 21 = 49 - 28 - 21 = 21 - 21 = 0

  3. Complete the table with the calculated values.

    x−4−3−2−1012345678y110−9−16−21−24−25−24−21−16−9011\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline y & 11 & 0 & -9 & -16 & -21 & -24 & -25 & -24 & -21 & -16 & -9 & 0 & 11 \\ \hline \end{array}

    The completed table is shown above.

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