### Home > CCA > Chapter 10 > Lesson 10.3.2 > Problem 10-125

10-125.

Joaquin needed to find the maximum value of

*y*= −*x*^{2}+ 4*x*− 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 −x*^{2}.”“

*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*).