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Home > A2C > Chapter 7 > Lesson 7.2.2 > Problem 7-117

7-117.
  1. 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 ✎

    1. f (x) = 4x2 − 12x + 6

    2. 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).