If the vertex of y=axˆ2+bx+c is at (0,-7) and a>0, select the true statement about min and max

Question

If the vertex of y=axˆ2+bx+c is at (0,-7) and a>0, select the true statement

The minimum is -7

The maximum is 0

The maximum is -7

The minimum is 0

please explain your steps i am so lost

Answer 1

The parabola y = ax² + bx + c

Vertex is (0, - 7)

Vertex is the minimum or maximum point of parabola.

When a  is positive number the parabola opens up and has minimum value.

When a  is negative number the parabola opens down and has maximum value.

In this case a > 0

So it was upward parabola.

In the minimum point x  = 0 and y = - 7  so the graph of parabola cannot be lower than  -7.

The minimum value of y = - 7 occurs at x = 0.

The minimum is - 7 .

First option is correct.