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Choose all of the following equations that have a vertex that is the minimum point of the parabola. More than one answer may be chosen. y = 2x2 + 2x + 8 y = −16x2 + 2x − 4 y = −x2 − 4x − 3 y = x2 + 2x + 4

Mathematics
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can you explain how to do this?
We need to know if the parabolas open up or down. If they open up, then they have a minimum value at the vertex. A parabola opens up if the coefficient to the a-term is positive. Notice that a is positive for y = 2x2 + 2x + 8 y = x2 + 2x + 4 and a is negative for y = −16x2 + 2x − 4 y = −x2 − 4x − 3 Thus, y = 2x2 + 2x + 8 y = x2 + 2x + 4 have vertices that are minimum points of the their parabolas.

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