### Home > CCA2 > Chapter 10 > Lesson 10.1.2 > Problem10-40

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 ✎

1. $f(x) = x^2 + 6x + 7$

1. $f(x) = x^2 - 10x$

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?

$f(x) - 7 = x^2 + 6x$

$f(x) + 2 = x^2 + 6x + 9$

$f(x) + 2 = (x + 3)^2$

$f(x) = (x + 3)^2 - 2$

Follow the steps outlined in part (a).