Prentice Hall's Online Lesson Quiz Enter Web Code: aga–0501
A quadratic function is a function that can be written in standard form. Equations of second degree are called quadratic.
|
Since the largest exponent of the variable is 2, we say that a quadratic equation has a degree of 2. Notice that a quadratic equation contains only one variable, and all of the exponents are positive integers.
In a quadratic function, ax2 is called the quadratic
term, bx is the linear term,
and c is the constant term. The
function, for example,
is in
quadratic form. The quadratic term is 3x2, the linear
term is –4x, and the constant term is 7.
example 1: |
Write the given function in quadratic form. Identify the quadratic term, the linear term, and the constant term. |
|
|
|
|
|
The quadratic term is x2 , the linear term is 8x, and the constant term is 3. |
Graphs of quadratic functions are called parabolas. In this section we explore some basic methods of graphing parabolas. Previous courses may have taught you to graph any function by creating a table of values. This can be accomplished by choosing any x-values you desire and substituting these values into the equation to find corresponding y-values, then plotting the points and connecting the points to create the graph. An example follows.
The parent graph f(x) = x2 is shown below.
|
|
|||||||||||||||||||
|
In the example shown above, the point (0, 0) on the graph is called the vertex of the parabola. The vertex is the maximum or the minimum point of a parabola. In this example, the vertex is the minimum point. The y-axis is the axis of symmetry for the graph. We should notice the points, other than the vertex, occur in pairs that have the same y-coordinate. If you fold the graph along the axis of symmetry, the two sides of the parabola coincide.
