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.

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