Joaquin needed to find the maximum value of y = −x2 + 4x − 1 but was stuck. Homework Help ✎
“No problem,”said Thao. “The parabola opens downward so just complete the square to find the vertex. The y-value of the vertex will be the maximum.”
“I know that,” said Joaquin. “The problem is that it is −x2.”
“Mmm…what if we multiply everything by –1? Can we now complete the square?”
Multiply the equation by –1 so you have −y = ....
Complete the square on the right side.
Multiply the equation by –1 so you are back to y = ...
Identify the vertex and the maximum value.
Each term should have the opposite sign.
−y = (x − 2)2 − 3
y = −(x − 2)2 + 3
If y = a(x − h)2 + k, then the vertex is at (h, k).