Question

Explain how the sign of a in the equation y=a(x-h)^2 + k tells you whether the parabola has a minimum or maximum value.

Answer 1

in short, for a vertical parabola, namely one whose independent variable is on the x-axis, usually is x², if the leading term coefficient is negative, the parabola opens downward, and its peak or vertex is at a maximum, check the picture below at the left-hand-side.

and when the leading term coefficient is positive, the parabola opens upwards, with a minimum, check the picture below at the right-hand-side.