Page 784 - Algebra 1

L E S S O N Interpreting the Discriminant 113
Warm Up
1. Vocabulary The is the number or expression under a radical
New Concepts
(13)
symbol.
Evaluate each expression for the given values. 2. -x2 - xy - y for x = -5 and y = -1
(9)
3. b2 + 3ab - a for a = -7 and b = -2 (9)
4. ab - 5b2 for a = 3 and b = 4 (9)
5. 7y2z + 9 for y = -3 and z = -1 (9)
The quadratic formula is one method used to solve quadratic equations. Recall the quadratic formula for a quadratic equation of the form
ax2 + bx + c = 0 is:
x=
In the formula, the expression under the radical sign, b2 - 4ac, is called the
discriminant.
Consider the graphs below and the value of the discriminant for each equation. 0=x2 -4x+3
b2 - 4ac a = 1, b = -4, c = 3
= (-4)2 - 4(1)(3) Substitute.
=4
There are 2 x-intercepts. The discriminant is positive.
0=x2 -4x+4
b2 - 4ac a = 1, b = -4, c = 4
=(-4)2 - 4(1)(4) Substitute.
=0
There is one x-intercept. The discriminant is zero.
0=x2 -4x+5
b2 - 4ac a = 1, b = -4, c = 5 (-4)2 - 4(1)(5) Substitute.
= -4
There are no x-intercepts. The discriminant is negative.
- b ± √ b 2 - 4 a c __
2a
O
4
8
-4
-8
y
4
x
-8
-4
4
8
-4
-8
y
4
O
x
-8
-4
4
8
-4
Online Connection www.SaxonMathResources.com
4
y
O
x
-8
-4
-8
Lesson 113 769