Question

Which equation does the graph of the systems of equations solve? quadratic graph opening down and quadratic graph opening up. They intersect at negative 4, 0 and negative 3, negative 1.
x2 − 2x + 8 = x2 − 8x − 16
x2 + 6x + 8 = −x2 − 8x − 16
−x2 − 2x + 8 = 2x2 − 8x − 16
−x2 − 2x + 8 = 2x2 − 8x + 16

Answer 1

The quadratics of the 2nd choice are the only ones that go through both points (-4, 0) and (-3, -1).

x² +6x +8 = -x² -8x -16

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The quadratic with those two points as solution will be of the form
.. a(x +4)(x +3) = 0
.. a(x^2 +7x +12) = 0
When you subtract one side or the other to put the equation in this form, only the 2nd selection matches:
.. 2(x^2 +7x +12) = 0