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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
1. Graphing Quadratic Functions
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Exercise 68 Page 102

The line x=- b2a is an axis of symmetry for the graph of a quadratic function in the form y=ax^2+bx+c.

Example Answer: y=4x^2+3x

Practice makes perfect

We want to write a quadratic function for which the graph has an axis of symmetry of x=- 38. Let's use the formula for the graph of a quadratic function in the form y=ax^2+bx+c.

Let's compare the formula, x=- b2a, with the axis we want to have, x=- 38.

-b/2a=-3/8
MultEqn

LHS * (- 1)=RHS* (- 1)

b/2a=3/8
MultEqn

LHS * 2=RHS* 2

b/a=3/4

We can choose b to be 3 and a to be 4, but please note that there is more than one possibility. Since there is no variable c in the formula for the axis of symmetry, x=- b2a, we can substitute any value we want for c. For simplicity, let's choose c= 0. Now we will write the quadratic function. y= ax^2+ bx+ c ⇓ y= 4x^2+ 3x+ 0=4x^2+3x An example quadratic function for which the graph has an axis of symmetry of x=- 38 is y=4x^2+3x.

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