Page 799 - Algebra 1

Example
3
Solving Cubic Equations Using a Graphing Calculator
Solve -2x2 = _1 x3 - 1 by graphing on a graphing calculator. 2
SOLUTION
W r i t e - 2 x 2 = _1 x 3 - 1 s o t h a t o n e s i d e i s e q u a l 2
to zero. Then graph the related function and find its x-intercepts.
Graphing Calculator Tip
For help with graphing functions, refer to the graphing calculator keystrokes in Lab 3 on p. 305.
Adding 2x2 to both sides of the original equation gives the equation 0 = _1 x3 + 2x2 - 1.
2
Use the graphing calculator to graph the related
functiony=_1x3 +2x2 -1. 2
The graph shows that there are three x-intercepts. Trace to estimate their values.
The approximate solutions are x ≈ -3.9, x ≈ -0.8, and x ≈ 0.7.
For better estimates, use the Zero function. To the nearest hundredth, the solutions are x ≈ -3.87, x ≈ -0.79, and x ≈ 0.66.
Application: Volume of a Cube
A cube of pure gold weighing 100 pounds would have a volume of about 143 cubic inches. Use a graphing calculator to estimate the side length of a 100-pound cube of gold.
SOLUTION
The formula for the volume of a cube is V = s3. To graph this equation on a graphing calculator,
let y represent V and x represent s. Then graph y = x3.
Adjust the window to make sure that 143 is included in the y-values.
Window Settings Xmin = 0
Xmax = 12 Ymin = 0
Ymax = 200
Trace to estimate the x-value where y = 143. When y = 143, x ≈ 5.2.
The side length of a cube of gold weighing 100 pounds would be about 5.2 inches—about the width of a DVD case.
Math Language
Remember that the zeros of a function are its x-intercepts or solutions.
Example
4
784 Saxon Algebra 1