12.1. Solving a Quadratic Equation Graphically and by Calculator
Recall that a polynomial equation is one in which all powers of x are positive integers. A quadratic equation is a polynomial equation of second degree. That is, the highest power of x in the equation is 2. It is common practice to refer to a quadratic equation simply as a quadratic.
Example 1:The following equations are quadratic equations:

A quadratic function is one whose highestdegree term is of second degree.
Example 2:The following functions are quadratic functions:

Some quadratic equations have a term missing. A quadratic that has no x term is called a pure quadratic; one that has no constant term is called an incomplete quadratic.
Example 3:

12.1.1. Solving a Quadratic Graphically
We will show several ways to solve a quadratic; first graphically and by calculator, and, in the next section, by formula.
▪ Exploration:
In our chapter on graphing we plotted the quadratic function
 f(x) = x^{2} − 4x − 3
getting a curve that we called a parabola.
Try this. Either graph this function again or look back at our earlier graph. Does the curve intercept the x axis, and if so, how many times? Can you imagine a parabola that has more xintercepts? Zoom out far enough to convince yourself that the curve will not ...
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