Home > A2C > Chapter 7 > Lesson 7.2.2 > Problem 7-117
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. Homework Help ✎
f (x) = 4x2 − 12x + 6
g(x) = 2x2 + 14x + 4
Make the coefficient of x² equal to 1 by factoring out a 4 in the first two terms.
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 ( )'s and subtract the equivalent '9' outside the ( )'s on the same side.
Then simplify.
f(x) = 4(x2 − 3x) + 6
f(x) = 4(x² − 3x + 2.25) + 6 −9
f(x) = 4(x − 1.5)2 − 3
See part (a).