Chapter 9. Quadratic Equations

In this chapter, you explore the quadratic equation. This equation is a polynomial of the second degree and generates a parabola. The standard form of the quadratic equation reads ax² + bx + c. In the same way that you could change the shape and position of sets of lines used to graph absolute values, you can also change the shape and position of the parabolas you create using quadratic equations. You can make the parabola narrower or wider by changing the coefficient of the x variable. You translate the parabola along the x axis by interpreting x as x – h, where h establishes the line of symmetry for the parabola. You can also shift the parabola up and down the y axis by using a value that corresponds to c in the standard formula. To solve for the x-intercepts of a quadratic equation, you can start by completing the square. You can also use the quadratic formula. Such topics provide many interesting ways to interpret events mathematically. Among the topics that you examine as you explore how this is so are the following:

• How to define a quadratic equation in its standard form

• Reviewing the notions of constant and changing slopes

• How to make a parabola narrower or wider

• Translating a parabola along the x axis

• Making a parabola so that it opens downward

• Completing squares and the quadratic formula