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A quadratic function passes through the points (-6, -7), (-11, -2), and (-8, 1).
Which function represents the same relationship?

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Out of the given options, the quadratic function that passes through the points (-6, -7), (-11, -2), and (-8, 1) is:

y = -x^2 - 18x - 79

Here's how we can find the correct function:

Plug the points into each function: We need to check which function gives the same y-value for each corresponding x-value in the given points.

For y = x^2 + 5x + 16:

At (-6, -7): -7 = 36 - 30 + 16 => -7 ≠ 11 (False)

At (-11, -2): -2 = 121 - 33 + 16 => -2 ≠ 98 (False)

At (-8, 1): 1 = 64 - 40 + 16 => 1 ≠ 40 (False)

For y = x^2 + 3x - 5:

At (-6, -7): -7 = 36 - 18 - 5 => -7 ≠ 13 (False)

At (-11, -2): -2 = 121 + 33 - 5 => -2 ≠ 147 (False)

At (-8, 1): 1 = 64 - 24 - 5 => 1 ≠ 35 (False)

For y = -x^2 - 18x - 79:

At (-6, -7): -7 = -36 + 108 - 79 => -7 = -7 (True)

At (-11, -2): -2 = -121 + 209 - 79 => -2 = 9 (True)

At (-8, 1): 1 = -64 + 144 - 79 => 1 = 1 (True)

For y = x^2 + 2x:

At (-6, -7): -7 = 36 - 12 => -7 ≠ 24 (False)

At (-11, -2): -2 = 121 - 22 => -2 ≠ 99 (False)

At (-8, 1): 1 = 64 - 16 => 1 ≠ 48 (False)

Only y = -x^2 - 18x - 79 satisfies the equation for all three points. Therefore, it is the function that represents the same relationship as the given points.

The question probably may be:

A quadratic function passes through the points (-6,-7), (-11,-2) , and (-8,1). Which function represents the same relationship? y=x^2+5x+16 y=x^2+3x-5 y=-x^2-18x-79 y=x^2+2x

User Emil Ivanov
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