### Home > CCA2 > Chapter 10 > Lesson 10.1.2 > Problem 10-40

10-40.

Complete the square to convert each of the following quadratic functions to graphing form. State the vertex and sketch the graph. Homework Help ✎

*f*(*x*) =*x*^{2}+ 6*x*+ 7*f*(*x*) =*x*^{2}− 10*x*

Move the constant to the other side.

Determine what number should be added to both sides so that the right side is factorable as (*x* − *h*)^{2}.

Add 9 to both sides.

Factor the right side of the equation.

Move the '2' back to the right side.

Vertex: (−3, −2) Why/how do you know?

*f*(*x*) − 7 = *x*^{2} + 6*x*

*f*(*x*) + 2 = *x*^{2} + 6*x* + 9

*f*(*x*) + 2 = (*x* + 3)^{2}

*f*(*x*) = (*x* + 3)^{2} − 2

Follow the steps outlined in part (a).