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Malik is graphing a parabola given by the equation y=−14x2+3x−6

. Which table of ordered pairs would match this parabola?(1 point)
pick one

x-value y-value
−2
−6
−6
−10
−10
−6
x -value y -value negative 2 negative 6 negative 6 negative 10 negative 10 negative 6

x-value y-value
2 −1
6 3
10 −1
x -value y -value 2 negative 1 6 3 10 negative 1

x-value y-value
4 −4
2 −3
0 −4
x -value y -value 4 negative 4 2 negative 3 0 negative 4

x-value y-value
0 −1
−4
−5
−8
−1
x -value y -value 0 negative 1 negative 4 negative 5 negative 8 negative 1
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1 answer

To find the ordered pairs that match the parabola given by the equation \( y = -14x^2 + 3x - 6 \), we can substitute the x-values from each option into the equation and see if the resulting y-values match those provided in the options.

Let’s evaluate each table option:

  1. Option 1:

    • For \( x = -2 \): \[ y = -14(-2)^2 + 3(-2) - 6 = -14(4) - 6 - 6 = -56 - 6 - 6 = -68 \]
    • For \( x = -6 \): \[ y = -14(-6)^2 + 3(-6) - 6 = -14(36) - 18 - 6 = -504 - 18 - 6 = -528 \]
    • For \( x = -10 \): \[ y = -14(-10)^2 + 3(-10) - 6 = -14(100) - 30 - 6 = -1400 - 30 - 6 = -1436 \]

  2. Option 2:

    • For \( x = 2 \): \[ y = -14(2)^2 + 3(2) - 6 = -14(4) + 6 - 6 = -56 + 6 - 6 = -56 \]
    • For \( x = 6 \): \[ y = -14(6)^2 + 3(6) - 6 = -14(36) + 18 - 6 = -504 + 18 - 6 = -492 \]
    • For \( x = 10 \): \[ y = -14(10)^2 + 3(10) - 6 = -14(100) + 30 - 6 = -1400 + 30 - 6 = -1376 \]

  3. Option 3:

    • For \( x = 4 \): \[ y = -14(4)^2 + 3(4) - 6 = -14(16) + 12 - 6 = -224 + 12 - 6 = -218 \]
    • For \( x = 2 \): \[ y = -14(2)^2 + 3(2) - 6 = -14(4) + 6 - 6 = -56 + 6 - 6 = -56 \]
    • For \( x = 0 \): \[ y = -14(0)^2 + 3(0) - 6 = -6 \]

  4. Option 4:

    • For \( x = 0 \): \[ y = -6 \]
    • For \( x = -4 \): \[ y = -14(-4)^2 + 3(-4) - 6 = -14(16) - 12 - 6 = -224 - 12 - 6 = -242 \]
    • For \( x = -5 \): \[ y = -14(-5)^2 + 3(-5) - 6 = -14(25) - 15 - 6 = -350 - 15 - 6 = -371 \]
    • For \( x = -8 \): \[ y = -14(-8)^2 + 3(-8) - 6 = -14(64) - 24 - 6 = -896 - 24 - 6 = -926 \]

None of the evaluated points from the options match the outputs of the parabola given the equation \( y = -14x^2 + 3x - 6 \). Therefore, the correct answer is that none of the tables provided match the parabola described by the equation.

Please double check the values in the options or provide additional context if needed, as it appears there is no matched table.