Question

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

Answer 1

can you explain how to do this?

Answer 2

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.