CPM Homework Help : CCA2 Problem 10-40

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10-40.

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

$f(x) = x^2 + 6x + 7$
Step 1(a):
Move the constant to the other side.
$f(x) - 7 = x^2 + 6x$
Step 2(a):
Determine what number should be added to both sides so that the right side is factorable as $(x - h)^2$ .
Step 3(a):
Add $9$ to both sides.
$f(x) + 2 = x^2 + 6x + 9$
Step 4(a):
Factor the right side of the equation.
$f(x) + 2 = (x + 3)^2$
Move the ' $2$ ' back to the right side.
Answer (a):
Vertex: $(-3, -2)$ Why/how do you know?
$f(x) = (x + 3)^2 - 2$

$f(x) = x^2 - 10x$
Hint (b):
Follow the steps outlined in part (a).

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