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## by vhiggins1 on Nov 18, 2010

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• Quadratic Inequalities 5.7 Algebra 2
• Graphing Inequalities
• Draw the parabola and shade the area indicated by the inequality.
• Graphing Inequalities
• y > x 2 - 2x -3
• Use a graphing calculator to draw the parabola.
• (http://www.coolmath.com/graphit/)
• Graphing Inequalities
• y > x 2 - 2x -3
• Or use your notes from 5.1 :)
• Find the vertex and the axis of symmetry
• Graph both parabolas first using a graphing calculator .
• Graph both parabolas first.
• Then shade the areas indicated.
• Graph both parabolas first.
• Then shade the areas indicated.
• The solution to the system is the part that is shaded by all inequalities. (If there are no overlapping spots, there is no solution .)
• Solving Inequalities
• Solve the equation to find the “critical x-values.”
• x 2 + 2x  8  x 2 + 2x - 8  0
• Solve for 0.
• x 2 + 2x  8  x 2 + 2x - 8  0
• (x - 2)(x + 4)  0
• Factor.
• x 2 + 2x  8  x 2 + 2x - 8  0
• (x - 2)(x + 4)  0
• x - 2 = 0 and x + 4 = 0
• Solve for x.
• x = 2 and x = -4.
• Solving Inequalities
• Solve the equation to find the “critical x-values.”
• Plot the critical numbers on a number line.
0 -4 2
• Solving Inequalities
• Solve the equation to find the “critical x-values.”
• Plot the critical numbers on a number line.
• Notice that this breaks the number line up into 3 sections.
• Solving Inequalities
• Solve the equation to find the “critical x-values.”
• Plot the critical numbers on a number line.
• Test a number inside each region.
0 -4 2
• [-4, 2] is the solution.
• Use square brackets if “less than or equal to.” Use parentheses if just “less than” or “greater than.”