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