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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)

Responses

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

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

x-value y-value
2 −1
6 3
10 −1

1 answer

To find the correct table of ordered pairs that matches the parabola given by the equation \( y = -14x^2 + 3x - 6 \), we can replace the x-values in the equation with the x-values from each response and calculate the corresponding y-values.

  1. First table:

    • \( x = 0 \): \[ y = -14(0^2) + 3(0) - 6 = -6 \]
    • \( x = -4 \): \[ y = -14(-4^2) + 3(-4) - 6 = -14(16) - 12 - 6 = -224 - 12 - 6 = -242 \]
    • \( x = -8 \): \[ y = -14(-8^2) + 3(-8) - 6 = -14(64) - 24 - 6 = -896 - 24 - 6 = -926 \]
    • Result: This table does not match.

  2. Second table:

    • \( x = -2 \): \[ y = -14(-2^2) + 3(-2) - 6 = -14(4) - 6 - 6 = -56 - 6 - 6 = -68 \]
    • \( x = -6 \): \[ y = -14(-6^2) + 3(-6) - 6 = -14(36) - 18 - 6 = -504 - 18 - 6 = -528 \]
    • \( x = -10 \): \[ y = -14(-10^2) + 3(-10) - 6 = -14(100) - 30 - 6 = -1400 - 30 - 6 = -1436 \]
    • Result: This table does not match.

  3. Third table:

    • \( x = 4 \): \[ y = -14(4^2) + 3(4) - 6 = -14(16) + 12 - 6 = -224 + 12 - 6 = -218 \]
    • \( x = 2 \): \[ y = -14(2^2) + 3(2) - 6 = -14(4) + 6 - 6 = -56 + 6 - 6 = -56 \]
    • \( x = 0 \): \[ y = -14(0) + 0 - 6 = -6 \]
    • Result: This table does not match.

  4. Fourth table:

    • \( x = 2 \): \[ y = -14(2^2) + 3(2) - 6 = -14(4) + 6 - 6 = -56 + 6 - 6 = -56 \]
    • \( x = 6 \): \[ y = -14(6^2) + 3(6) - 6 = -14(36) + 18 - 6 = -504 + 18 - 6 = -492 \]
    • \( x = 10 \): \[ y = -14(10^2) + 3(10) - 6 = -14(100) + 30 - 6 = -1400 + 30 - 6 = -1376 \]
    • Result: This table does not match.

Upon reviewing, all calculations show that none of the given ordered pairs correspond to the values that solve the equation \( y = -14x^2 + 3x - 6 \). It looks like the calculations were not producing values that aligned with any ordered pairs, which you might expect from easy integer values input in tables.

To ensure success on your test: Re-check pairs against the given equation, and if calculators are allowed, one may wish to double-check results.

If asked directly for a response based on the given tables, please provide context or verify further pairs for potential value insertions to catch a match (if one exists, likely one with rounded integer points).