Page 757 - Algebra 1

L E S S O N Using the Quadratic Formula 110
Warm Up
New Concepts
1. Vocabulary A equation can be written in the form (84) ax2 + bx + c = 0, where a is not equal to 0.
Find the value of c to complete the square for each expression. 2.x2 +8x+c 3.x2 +9x+c
(104) (104)
4. Solve x2 + 10x = 24 by completing the square. Check your answer. (104)
Different methods are used to solve quadratic equations. One method is applying the quadratic formula. The quadratic formula is derived by completing the square of the standard form of the quadratic equation ax2 +bx+c=0.
ax2 +bx+c=0
_2 __
ax + bx + c = 0 Divide by the coefficient of x2. aaa
Math Language
A quadratic equation is an equation whose graph is a parabola.
___
x2 + bx = - c Subtract the constant c from both
aaa sides.
__2__2_
x2 + bx + ( b ) = - c + ( b ) a 2a a 2a
Add ( b )2 to complete the square. 2a
Simplify.
Write the left side as a squared binomial and the other side with the LCD.
Take the square root.
_ _2 _ _2 x2+bx+ b =-c+ b
a 4a2 a 4a2 ( b )2 b2 - 4ac
__ x + 2a = 4a2
__ √x + 2a = ±√ 4a
( b )2 b2 - 4ac
x+ b =±√ b2 - 4a c __
2
Simplify. x= 2a Solve.
2a _2a_
- b ± √ b 2 - 4 a c
Quadratic Formula
For the quadratic equation ax2 + bx + c = 0, - b ± √ b 2 - 4 a c
__
x = 2a when a ≠ 0.
Online Connection www.SaxonMathResources.com
The quadratic formula can be used to solve any quadratic equation.
742 Saxon Algebra 1