Page 846 - Algebra 1

A quadratic inequality in one variable can be written in four different forms ax2 +bx+c<0 ax2 +bx+c≤0
ax2 +bx+c>0 ax2 +bx+c≥0
Quadratic inequalities can be solved using tables, graphs, or algebraic methods.
Solving with a Table
Solve x2 - 2x ≤ 3 using a table.
SOLUTION
Step 1: Write the inequality as x2 - 2x - 3 ≤ 0. Step 2: Make a table of values.
The inequality x2 - 2x - 3 ≤ 0 is true for values of x between -1 and 3 inclusively. The solution of the inequality is -1 ≤ x ≤ 3.
Solving with a Graphing Calculator Table
Solve x2 - x - 4 ≤ 2 using a graphing calculator. SOLUTION
Step 1: Use a graphing calculator to graph each side of the inequality. Set Y1equaltox2 -x-4andsetY2equalto2.
Step2: Viewthetablecomparingthetwoequations.
Step3: Identifythevaluesof xwhereY1=x2 -x-4arelessthanor
equal to the values of Y2 = 2. The solution set is -2 ≤ x ≤ 3.
Example
2
x
-5
-4
-3
-2
-1
0
1
2
3
4
5
x2 -2x-3
32
21
12
5
0
-3
-4
-3
0
5
12
Example
3
Appendix Lesson 1 831
APPENDIX LESSONS