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 = ax2 + 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 x2 + bx + c = 0, splitting the expression into two binomials and using the zero product property to solve the equation.
Not all equations
ax2 + 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 = ax2 + 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.
