Algebra 2 Bell Ringer:
Evaluate the expression:
b2 – 4ac when a = -5, b = 2, c = 4
Algebra 2 Bell Ringer:
Evaluate the expression:
b2 – 4ac when a = -5, b = 2, c = 4
= 84
The Discriminant
Algebra 2
Mr. Peebles
Fall 2012
Objectives
Wednesday November 28, 2012
Daily Learning Target (DLT)
“I can apply and remember the
discriminant to determine the nature of the
roots of a quadratic equation.”
Note:
These three examples demonstrate a
pattern that is useful in determining the
nature of the root of a quadratic equation.
In the quadratic formula, the expression
under the radical sign, b2 – 4ac is called
the discriminant given ax2 + bx + c = 0.
The discriminant tells the nature of the
roots of a quadratic equation.
Ex. 1: Solve t2 – 3t – 28 = 0
Find The Discriminant:
a = 1 b = -3 c = -28
(-3)2 – 4(1)(-28)
9 – (-112) = 121
b2 – 4ac
Fist-To-Thumbs?
Ex. 2: Solve x2 – 8x + 16 = 0
Find The Discriminant:
b2 – 4ac
a = 1 b = -8 c = 16
(-8)2 – 4(1)(16)
64 – 64 = 0
There is 1 distinct root—Real and rational.
Fist-To-Thumbs?
Ex. 3: Find the value of the discriminant of the
equation.
2x2 + x = 3
(Hint: Equation must equal 0)
2x2 + x – 3 = 0 (Subtract 3 on both sides)
a = 2 b = 1 c = -3
b2 – 4ac = (1)2 – 4(2)(-3)
= 1 + 24
= 25
Fist-To-Thumbs?
Ex. 4: Find the value of the discriminant of the
equation.
x2 + 8 = 0
a=1 b=0 c=8
b2 – 4ac = (0)2 – 4(1)(8)
= 0 – 32
= – 32
Fist-To-Thumbs?
Assignment
Work on the Kuta Discriminant Worksheet
Algebra 2 Closer:
Find the discriminant for equation:
3x2 – 5x = 2
Algebra 2 Closer:
Find the discriminant for equation:
3x2 – 5x = 2
= 49