Solve Quadratic Equations By The Quadratic Formula Worksheet - Chapter 10.6 Page 7
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7ACTIVITY
ACTIVITY
Investigating
Investigating
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Algebra
Algebr
a r r
Use before Lesson 10.7
10.7
The Discriminant
Q
How can you determine the number of solutions of a
U E S T I O N
quadratic equation?
}
Ï
2b 6
2
2 4ac
b
In the quadratic formula, x 5
2
2 4ac is called
}}
, the expression b
2a
the discriminant.
E
Determine how the discriminant is related to the number of
X P L O R E
solutions of a quadratic equation
STEP 1
Find the number of solutions
y 5 x
2 6x 1 12
2
Find the number of solutions of the equations below
by finding the number of x-intercepts of the graphs
of the related functions.
0 5 x
2
2 6x 2 7
0 5 x
2
2 6x 1 9
2
0 5 x
2
2 6x 1 12
y 5 x
2 6x 1 9
2
8
2
2 4ac
Find the value of b
STEP 2
For each equation in Step 1, determine whether the value of
2
2 4ac is positive, negative, or zero.
b
Make a table
STEP 3
Organize your results from Steps 1 and 2 in a table as shown.
y 5 x
2 6x 2 7
2
2
2 4ac
Equation
Number of solutions
Value of b
2
0 5 x
2 6x 2 7
?
?
2
0 5 x
2 6x 1 9
?
?
2
0 5 x
2 6x 1 12
?
?
Make a conjecture
STEP 4
Make a generalization about the value of the discriminant and
the number of solutions of a quadratic equation.
D
C
Use your observations to complete these exercises
R A W
O N C L U S I O N S
2
1 4x 2 5 5 0,
1.
Repeat Steps 123 using the following equations: x
2
1 4x 1 4 5 0, and x
2
1 4x 1 6 5 0. Is your conjecture still true?
x
2
2 4ac is under the radical sign in the
2.
Notice that the expression b
quadratic formula. Use this observation to explain why the value of
2 4ac determines the number of solutions of a quadratic equation.
2
b
677
10.7 Interpret the Discriminant
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