The Quadratic Formula.
11
The Quadratic Formula. a ac b b x 2 4 2 Lesson 9.8
description
The Quadratic Formula. Lesson 9.8. Warm Up Evaluate for x = –2, y = 3, and z = –1. . 1. x 2. 4. 2. xyz. 6 . 3. x 2 – yz. 4. y – xz. 7. 1 . 6. z 2 – xy. 5. – x. 7 . 2. California Standards. - PowerPoint PPT Presentation
Transcript of The Quadratic Formula.
The Quadratic Formula.
aacbbx
242
Lesson 9.8
Warm UpEvaluate for x = –2, y = 3, and z =
–1. 6 1. x2 2. xyz
3. x2 – yz 4. y – xz 4
5. –x 6. z2 – xy
7 1
7 2
California Standards
19.0 Students know the quadratic formula and are familiar with its proof by completing the square. 20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.
In the previous lesson, you completed the square to solve quadratic
equations. If you complete the square of ax2 + bx + c = 0, you can derive
the Quadratic Formula.
What Does The Formula Do ?
The Quadratic formula allows you to find the roots of a quadratic equation (if they exist) even if the quadratic equation does not factorise.The formula states that for a quadratic equation of the form :ax2 + bx + c = 0 The roots of the quadratic equation are given by :
aacbbx
242
Example 1
Use the quadratic formula to solve the equation :x 2 + 5x + 6= 0Solution:x 2 + 5x + 6= 0a = 1 b = 5 c = 6
aacbbx
242
12)614(55 2
x
2)24(255
x
215
x
215
215
xorx
x = - 2 or x = - 3
These are the roots of the equation.
Example 2
Use the quadratic formula to solve the equation :8x 2 + 2x - 3= 0
Solution:8x 2 + 2x - 3= 0a = 8 b = 2 c = -3
aacbbx
242
82)384(22 2
x
16)96(42
x
161002
x
16102
16102
xorx
x = ½ or x = - ¾ These are the roots of the equation.
Example 3Use the quadratic formula to solve the equation :8x 2 - 22x + 15= 0Solution:8x 2 - 22x + 15= 0a = 8 b = -22 c = 15
aacbbx
242
82)1584()22()22( 2
x
16)480(484(22
x
16422
x
16222
16222
xorx
x = 3/2 or x = 5/4 These are the roots of the equation.
Because the Quadratic Formula contains a square root, the solutions may be irrational. You can give the exact solution by leaving the square root in your answer, or you can approximate the solutions.
1. Solve x2 + x = 12 by using the Quadratic Formula.
2. Solve –3x2 + 5x = 1 by using the Quadratic Formula.
3. Solve 8x2 – 13x – 6 = 0. Use at least 2 different methods.
Lesson Quiz
3, –4
= 0.23, ≈ 1.43
