3.6 The Discriminant
negative
positive
b2 - 4ac
zero
Summary
Number of Real Solutions
2
?
0
?
1
?
Find the discriminant and determine the number of real solutions.
1.  y = -2x2 + 4x - 4
2.  y = -x2 - 6x - 6
3.  y = 2x2 - 8x + 8
4.  y = x2 - 6x + 13
6.  y = -2x2 + 4x - 1
5.  y = x2 - 6x + 9
Equation
b2 - 4ac
Number of Real Zeros 
         (0, 1, or 2)
y = x2 + 2x + 0
y = -x2 - 6x -12
Graph
no solutions
?
x = -2 or 0
?
Solutions
Number of RealSolutions
    0
(none)
?
2
?
Value ofb2 - 4ac
-12
?
4
?
Is b2 - 4acpositive, negative, or zero?
positive
?
negative
?
y = -x2 - 6x - 13
y = 2x2 - 4x + 2
Graph
No solutions
?
Solutions
x = 1
?
Number of RealSolutions
   0(none)
?
1
?
Value ofb2 - 4ac
0
?
-16
?
Is b2 - 4acpositive, negative, or zero?
negative
?
zero
?
y = x2 - 8x + 16
y = -x2 + 8x - 12 
Graph
Solutions
x = 2 or 6
?
x = 4
?
Number of RealSolutions
2
?
1
?
Value ofb2 - 4ac
16
?
0
?
Is b2 - 4acpositive, negative, or zero?
positive
?
zero
?
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