CPM Homework Help : CCA2 Problem 12-57

Rewrite $f(x) = 2x^2 - 4x + 1$ in graphing form. State its domain, range, vertex and line of symmetry. Include a labeled sketch as part of your solution.

Step 1:

Multiply the equation by ¹/₂ so that the $x^²$ term has a coefficient of $1$ .

$\frac{1}{2}f(x)\ =\ x^2-2x+\frac{1}{2}$

Step 2:

Complete the square to factor the polynomial.

$\frac{1}{2}f(x)\ =\ (x^2-2x+1) +\frac{1}{2}-1$

$\frac{1}{2}f(x)\ =\ (x^2-2x+1) -\frac{1}{2}$

Answer:

$f(x)\ =\ 2(x-1)^2-1$

Hint:

Use the graph of the function below to help you find the domain, range, vertex, and line of symmetry.

Upward parabola, vertex at the point (1, comma negative 1), passing through the point (0, comma 1).