Maximum or Minimum

$y = {x}^{2}-4$ opens up, like a cup. Its vertex is its lowest point. $y = -{x}^{2}+4$ is the dashed curve. It opens down, like a hill. Its vertex is its highest point. The sign of a tells you which.

• $a > 0$: the height of the vertex is the minimum, the smallest output.
• $a < 0$: the height of the vertex is the maximum, the largest output.

The highest point of a thrown ball is a vertex like this.