Download Unit 1 Day 12 Notes - Garnet Valley School District

Warm up
Algebra II/Trig Honors
Unit 1 Day 11: Graph and Solve Quadratic Inequalities
Objective: Graph quadratic inequalities and systems of quadratic inequalities to find all solutions
Big Ideas: Where solutions to equations are often a finite set of numbers, solutions to inequalities are
often ranges (or intervals) of numbers.
The solutions to an equation break the number line into intervals of solutions (or nonsolutions) to related inequalities.
A quadratic inequality in two variables can be written in any of the follow forms:
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The graph of any such inequality consists
of all solutions (x, y) of the inequality.
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Step 1: Graph the parabola with equation y  ax 2  bx  c .
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Make the parabola _____________ for inequalities with < or >
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Make the parabola _____________ for inequalities with <or >
Step 2: Test a point (x, y) inside the parabola to determine whether the point is a solution of the
inequality.
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A ____________ inequality statement means the point is in the solution set.
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A ____________ inequality statement means the point is not in the solution set.
Step 3: Shade the region inside the parabola if the point from Step 2 is a solution.
Shade the region outside the parabola if the point from Step 2 is not a solution.
Example 1: Graph a quadratic inequality
Graph y  x 2  3x  4
Example 2: Use a quadratic inequality in real life
A manila rope used for rappelling down a cliff can safely support a weight W (in pounds) provided
W  1480d 2 where d is the rope’s diameter (in inches). Graph the inequality.
System of Quadratic Inequalities – similar to graphing a system of linear inequalities
1) ________________________________________
2) ________________________________________
3) ________________________________________ - this is called the graph of the system
Example 3: Graph a system of quadratic inequalities
y  x 2  4
y  x 2  2x  3
A quadratic inequality in one variable can be written in any of the follow forms:
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You can solve quadratic inequalities using
tables, graphs, or algebraic methods.
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Example 4: Solve a quadratic inequality using a table
Solve x 2  x  6 using a table.
Graphing to Solve Inequalities
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Graph y  ax 2  bx  c
If the inequality symbol is <, identify the x-values where the graph lies below the x-axis
If the inequality symbol is >, identify the x-values where the graph lies above the x-axis
Example 5: Solve a quadratic inequality by graphing
Solve 2 x 2  x  4  0
Example 6: The number T of teams that have participated in a robot-building competition for high
school students can be modeled by T ( x)  7.51x 2  16.4 x  35.0 0  x  9 where x is the number of
years since 1992. For what years was the number of teams greater than 100?
Example 7: Solve a quadratic inequality algebraically
Solve x 2  2 x  15
1. Change the inequality
symbol to an equal sign.
2. Solve the quadratic equation.
3. Plot your answers on a
number line and test each
region in the original
inequality.
4. Shade the regions that are
true and write your final
answer as a compound
inequality.
HW: Page 70 #3-5, 6-27 (M3), 36, 40, 48-57 (M3)