5.7 Graphing and Solving Quadratic Inequalities

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5.7 Graphing and Solving Quadratic Inequalities

• Goal Graph quadratic inequalities in 2 variables
  and in 1 variable.

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Graphing a Quadratic Inequality in 2 Variables

• Draw the parabola with equation y ax² bx c.
  Make the parabola dashed for inequalities with
• gt or lt and solid for inequalities with or ?.
• Choose a point (x, y) inside the parabola and
  check whether the point is a solution of the
  inequality
• If it is a solution, shade the region inside the
  parabola. If not a solution, shade the region
  outside the parabola.

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Graphing a Quadratic Inequality

• Graph y gt x² - 2x - 3

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Graphing a Quadratic Inequality

• Graph y lt x² - 3x

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Graphing a System of Inequalities

• Graph the system
• y ? x² - 4
• y lt -x² - x 2

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Solving a Quadratic Inequality in 1 Variable

• To solve ax² bx c lt 0 (or 0), graph
• y ax² bx c and identify the values for
  which the graph lies below (or on and below) the
  x axis.
• To solve ax² bx c gt 0 (or ? 0), graph
• y ax² bx c and identify the values for
  which the graph lies above (or on and above) the
  x axis.

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Solving a Quadratic Inequality by Graphing

• Solve x² - 6x 5 lt 0

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Solving a Quadratic Inequality Algebraically

• Solve x² 2x 8

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Homework

• Pg. 303 304 23 16 all , 17 44 every 3rd