Download Systems Inequalities 4 - 1-Var Quad Ineq by Graphing_2

Math 20-1
Systems of Equations and Inequalities: Lesson #4
Quadratic Inequalities in One Variable: Graphing
Objective: By the end of this lesson, you will be able to:
An inequality is
You can solve a linear inequality just like a linear equation, with just one extra rule:
e.g. 1) Solve the inequality 7  3x  25 . Graph the solution on a number line.
A quadratic inequality is
Quadratic inequalities are a bit more complicated to solve. We will learn 3 different methods.
Method 1:

Start by moving all the terms to the ________ side of the inequality, so that you have 0
on the right side.
In a quadratic inequality, we are looking for the where the graph is either _____________ or
___________ the x-axis.

If the inequality has > 0, look for the x-values where the graph is:

If the inequality has  0, look for the x-values where the graph is:

If the inequality has < 0, look for the x-values where the graph is:
Math 20-1
Systems of Equations and Inequalities: Lesson #4

If the inequality has  0, look for the x-values where the graph is:
The solution to a quadratic inequality is generally an __________________ (e.g. 10  x  2 ) or
more than one ___________________ (e.g. x  10 or x  2 ), not just a number. The solution
will have the same form of inequality signs as the __________________________________(i.e.
either < > or   ).
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e.g. 2) The graph below shows the function y   x 2  3 x . Use the graph to write the solutions
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to the following inequalities:
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a)  x 2  3 x  0
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b) 
3 2
x  3x  0
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e.g. 3) The graph below shows the function y  x 2  6 x  9 . Use the graph to write the solutions
to the following inequalities:
a) x 2  6 x  9  0
b) x 2  6 x  9  0
c) x 2  6 x  9  0
d) x 2  6 x  9  0
Math 20-1
Systems of Equations and Inequalities: Lesson #4
For most problems, you will not be given the graph. If this is the case, add these two steps to the
beginning of your solving process:

Find the roots of the equation algebraically.

Make a quick sketch of the graph, making sure the ______________________ are
accurate.
e.g. 4) Solve the quadratic inequality  2 x 2  9 x  4 by graphing. Graph the solution on a
number line.
e.g. 5) Write a quadratic inequality with the solution  5  x  3 .
Assignment:
p. 484-486 #1-2, 7, 15