Algebra 2
1
October 16, 2018
2.7: Solving Quadratic InequalitiesQuadratic Inequality: _____________________________________________________________________________________________________________
Example 1: Graphing Quadratic Inequalities in Two Variables Graph y < 2x2 4x + 6
Example 2: Solving Quadratic Inequalities by Using Tables or Graphs.Solve each inequality by using tables or graphs. a) x2 6x + 8 ≤ 3
* Use a graphing calculator to graph each side of the inequality. Y1 = x2 6x + 8 Y2 = 3
* Identify the values of x for which Y1 ≤ Y2.
b) x2 6x + 8 > 3
NOTES
Algebra 2
2
October 16, 2018
Example 3: Solving Quadratic Inequalities Using AlgebraSolve the inequality x2 4x +1 > 6 by using algebra.
Step 1: Write the related equation.
Step 2: Solve the equation for x to find the critical values.
Step 3: Test an xvalue in each interval.
Example 4: ProblemSolving Application.A business offers tours to the Amazon. The profit P that the company earns for x number of tourists can be modeled by P(x) = 25x2 +1000x 3000. How many people are needed for a profit of at least $5000?
Example 3b:Solve x2 + 7x + 6 ≤ 6