Page 798 - Algebra 1

The parent function for cubic polynomials is y = x3. The graph of y = -x3 is related to the graph of the parent function y = x3.
Graphing Cubic Functions
Evaluate the cubic parent function y = x3 and the function y = -x3 for x = -2, -1, 0, 1, and 2. Then graph the functions.
SOLUTION Make tables of values. Then plot points to graph the functions.
Example
1
Math Reasoning
Generalize Which transformation changes the graph of y = x3 into the graph of y = -x3?
x
-2
-1
0
1
2
y
-8
-1
0
1
8
8
y
4
y = x3
O
x
-8
-4
4
8
-8
y
x
-2
-1
0
1
2
y
8
1
0
-1
-8
=
Solving Cubic Equations by Graphing
a. Solve 0 = x3 - 1 by graphing. SOLUTION
To solve 0 = x3 - 1, begin by graphing the related function y = x3 - 1.
Then find the x-intercepts of y = x3 - 1 since these are the x-values where y = 0.
The only x-intercept is near 1, so the approximate solutionto0=x3 -1isx≈1.
b. Solve 2 = -2x3 - 7 by graphing. SOLUTION
Write2=-2x3 -7sothatonesideisequalto zero. Then graph the related function and find its x-intercepts.
Subtracting 2 from both sides of 2 = -2x3 - 7 gives the equation 0 = -2x3 - 9. To solve
0 = -2x3 - 9, graph the related function y=-2x3 -9.
The only x-intercept is between -1 and -2, at about -1.7. The approximate solution to 2 = -2x3 - 7 is x ≈ -1.7.
y
8
x3
4
x
-8
-4
4
8
-4
Example
2
Math Reasoning
Verify In Example 2a, how can you check whether x = 1 is the exact solution or not?
y
4
2
x
O
-4
-2
2
4
-4
y
Hint
Another way to solve
2 = -2x3 - 7 is to graph y = -2x3 - 7 and y = 2, and then to find the x value(s) at their point(s) of intersection.
4
O
x
-4
-2
-4
Lesson 115 783
2
4