CPM Homework Help : A2C Problem 7-117

Use the ideas developed in problem 7-116 to change each of the following quadratic equations into graphing form. Identify the vertex and the line of symmetry for each one.

$f \left(x\right) = 4x^{2} − 12x + 6$

Step 1(a):

Make the coefficient of $x²$ equal to 1 by factoring out a $4$ in the first two terms.

Step 2(a):

Take half of '3' and square it. You get: $\left(1.5\right)² = 2.25$ . The '4' indicates you really added 4(2.25) or 9. So add the 2.25 inside the ( )'s and subtract the equivalent '9' outside the ( )'s on the same side.

Then simplify.

Answer (a):

$f\left(x\right) = 4\left(x^{2} − 3x\right) + 6$

$f\left(x\right) = 4\left(x² − 3x + 2.25\right) + 6 −9$

$f\left(x\right) = 4\left(x − 1.5\right)^{2} − 3$

$g\left(x\right) = 2x^{2} + 14x + 4$
Hint (b):
See part (a).