Page 566 - Algebra 1

Example
1
Identifying Quadratic Functions
Determine whether each function represents a quadratic function.
a. y+7x=4x2 -6 SOLUTION
y+7x=4x2 -6
y=4x2 -7x-6 Solvefory.
It is a quadratic function because it can be written in the standard form of a quadratic equation.
b. y=5+2x SOLUTION
y = 5 + 2x
Since there is no quadratic term, it is not a quadratic function.
c. -2x3 +y=-5x3 +x2 SOLUTION
-2x3 +y=-5x3 +x2
y = -3x3 + x2 Add 2x3 to both sides.
Since there is a cubic term, it is not a quadratic function.
The graph of f(x) = x2 is known as the quadratic parent function. Graph the parent function by making a table of values. Plot the points and connect them with a smooth U-shaped curve called a parabola.
Graphing Quadratic Functions Using a Table
Use a table to graph the function. f(x) = -3x2
SOLUTION
Plot the points in a coordinate plane and draw a smooth curve through the points.
Math Reasoning
Write What type of function is related to the equation y = 5 + 2x? Describe the graph that represents the equation.
8
y
6
4
2
x
-4
-2
2
4
x
-4
-2
0
2
4
y
16
4
0
4
16
Example
2
Math Reasoning
Analyze Compare the widths of the graphs representing f(x) = x2 and f(x) = -3x2.
y
x
-4
-2
2
4
-4
-8
x
-2
-1
0
1
2
y
-12
-3
0
-3
-12
-12
Online Connection www.SaxonMathResources.com
Lesson 84 551