Introduction and Summary
This chapter deals with equations involving quadratic polynomials, i.e. polynomials of degree two. Quadratic equations are equations of the form y = ax 2 + bx + c or y = a(x - h)2 + k .
The shape of the graph of a quadratic equation is a parabola. The first section of this chapter explains how to graph any quadratic equation of the form y = a(x - h)2 + k , and it shows how varying the constants a , h , and k stretches and shifts the graph of the parabola.
The second section revisits factoring. In the last chapter, we learned how to factor expressions. Here, we factor equations of the form x 2 + bx + c = 0 , splitting the expression into two binomials and using the zero product property to solve the equation.
Not all equations ax 2 + bx + c = 0 can be easily factored. Thus, we need a formula to solve for x . This is the quadratic formula, and it is the focus of section three.
Finally, in the last section, we learn how to graph quadratic equations of the form y = ax 2 + bx + c by completing the square: adding and subtracting a constant to create a perfect square trinomial within our equation.
Though quadratic equations are just one type of polynomial, they are studied more in Algebra I and II than all other types of polynomials. They have unique properties that fascinate mathematicians, and they can be used as a model to understand more complex polynomials.