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) = x2 + 6x + 7
f(x) = x2 − 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 = x2 + 6x
f(x) + 2 = x2 + 6x + 9
f(x) + 2 = (x + 3)2
f(x) = (x + 3)2 − 2
Follow the steps outlined in part (a).