### Home > CCA2 > Chapter 6 > Lesson 6.2.2 > Problem6-119

6-119.

Use the ideas developed in problem 6-118 to change each of the following quadratic equations into graphing form. Identify the vertex and the line of symmetry for each one.

1. $f(x)=4x^2−12x+6$

Make the coefficient of $x^2$ equal to $1$ by factoring out a $4$ in the first two terms.

$f(x)=4(x^2−3x)+6$

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

$f(x)=4(x^2−3x+2.25)+6−9$

Then simplify.

$f(x)=4(x−1.5)^2−3$

2. $g(x)=2x^2+14x+4$

See part (a).