Download presentation

Presentation is loading. Please wait.

Published byEileen Powers Modified over 4 years ago

1
Ch 10: Polynomials G) Completing the Square Objective: To solve quadratic equations by completing the square.

2
Methods for Solving Quadratic Equations 1) Square Root Method (Works when no “x” term) 2) Graphic Method (Works when on lattice point) x=-1x=3 3) Quadratic Formula a=1 b= -2 c= -3 (Always works) 4) Factoring Method (Works when factorable) 5) Completing the Square (Always works) * * x = ±3 x = −1, x = 3

3
Rules 1)Subtract c from both sides….. 2)Divide both sides by a……… 3)Divide the x term by 2............ 4)Add b 2 to both sides…….. (the left side is a “perfect square”) 5) Square root both sides……….. 6) Solve for x …………………... ax 2 + bx + c = 0from Standard Form: ax 2 + bx = −c x 2 + b x = −c a a x + b 2a 2 = −c + b 2 2a + b 2 2a + b 2 2a x 2 + b x = −c 2a x + b 2a 2 −c + b 2 2a √√ = a a a a 2 a | x + b/(2a)| = a

4
6262 ( ) (x ) 2 = 7+ 3 2 = 9 + 9 Example 1 + 9 What number (c) makes this a Perfect Square?

5
Complete the perfect square trinomial -8 2 (x ) 2 = -5- 4 ( ) 2 = 16 + 16 Example 2

6
Complete the square Example 3

7
Complete the square Example 4

8
1) 2) Solve each equation by completing the square x 2 – 4x – 34 = -2 x 2 − 12x – 60 = 4 Classwork

9
3) 4) Solve each equation by completing the square x 2 + 8x – 26 = 7 2x 2 + 2x – 48 = 2 Classwork

10
5) 6) Solve each equation by completing the square x 2 + 2x + 16 = -2 x 2 − 8x + 21 = 6 Classwork

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google