CPM Homework Banner

Joaquin needed to find the maximum value of but was stuck.

“No problem,”said Thao. “The parabola opens downward so just complete the square to find the vertex. The -value of the vertex will be the maximum.”

“I know that,” said Joaquin. “The problem is that it is .”

Mmm…what if we multiply everything by ? Can we now complete the square?”

  1. Multiply the equation by so you have ....

    Each term should have the opposite sign.

  1. Complete the square on the right side.

  1. Multiply the equation by so you are back to ...

  1. Identify the vertex and the maximum value.

    If , then the vertex is at .