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```					Worksheet: Inequality of Quadratic Function                                          Royati Saha & LFS

Suppose we want to solve the quadratic inequality ax 2  bx  c  0 . This means we want to find
what values of x make the function f (x)  ax 2  bx  c positive.
So let’s sketch a graph of f (x) and see when it is positive. It is positive when the graph is above the
x-axis. So what information do we need to have a “good enough” sketch to get this information?
Investigation
1. Given that f(x) = x2 + x – 12. Determine the values of x so that f(x) ≥ 0.

f(x) = x2 + x – 12
Factor the function
f(x)= (x+4)(x-3)
Equate the factors to 0             (x+4)=0                      (x-3)=0

Solve the linear equations          x = -4                       x=3

Shape of the graph                  a=1>0 means Parabola that opens upward.
Sketch the graph

-4         3

f(x) ≥ 0
-4            3

State the domain                    x≤ -4 or x ≥ 3               (-∞,-4] , [3, ∞)

Algebra 2                                            1
Worksheet: Inequality of Quadratic Function                               Royati Saha & LFS

2. Given that f(x) = 8 – 2x - x2 . Determine the values of x so that f(x) ≤ 0.

Factor the function
Equate the factors to 0

Solve the linear equations

Shape of the graph
a. Sketch the graph.
b. Mark the x values where
f(x) ≤ 0 and

State the domain

3. Given that f(x) = x2 +2x-8. Determine the values of x so that f(x) ≥ 0.

Factor the function
Equate the factors to 0

Solve the linear equations

Shape of the graph
Sketch the graph and mark
the x values where f(x) ≤ 0.

State the domain

Algebra 2                                     2
Worksheet: Inequality of Quadratic Function                               Royati Saha & LFS

4. Given that f(x) = 7x - 2x2 – 3. Determine the values of x so that f(x) ≥ 0.

Factor the function
Equate the factors to 0

Solve the linear equations

Shape of the graph
Sketch the graph and mark
the x values where f(x) ≤ 0.

State the domain

5. Given that f(x) = 2x2 +7x+3. Determine the values of x so that f(x) < 0.

Factor the function
Equate the factors to 0

Solve the linear equations

Shape of the graph
Sketch the graph and mark
the x values where f(x) ≤ 0.

State the domain

Algebra 2                                     3
Worksheet: Inequality of Quadratic Function                                                    Royati Saha & LFS

6. Given that f(x) = x2 – 2x - 8. Determine the values of x so that f(x) > 0.

Factor the function
Equate the factors to 0

Solve the linear equations

Shape of the graph
Sketch the graph and mark
the x values where f(x) ≤ 0.

State the domain

Challenger questions:
7. Find the domain of the function g( x )  x 2  5x  6

1
8. Find the domain of the function g( x ) 
6  5x  x 2

( x  3)
9. Find the values of x such that f ( x )             0
( x  4)

x 4                         ( x  3)( x  4)
Hint: Multiple f ( x ) by         1  0 to get g( x )                   and notice
x 4                             ( x  4)2

x 4
(a) Since         1  0 , f ( x )  0 whenever g( x )  0 and
x 4

(b) g( x )  0 whenever ( x  3)( x  4)  0 and this we know how to solve!

( x  3)
10. Find the domain of f ( x )              . (Be careful to remove x  4 ).
( x  4)

Algebra 2                                                4

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