Download presentation

Published byEvan Richards Modified over 5 years ago

1
**Solving Quadratic Equations by Completing the Square**

2
**Perfect Square Trinomials**

Examples x2 + 6x + 9 x2 - 10x + 25 x2 + 12x + 36

3
**Rule for Completing the Square**

This is now a PST! So, it factors into this!

4
**Creating a Perfect Square Trinomial**

In the following perfect square trinomial, the constant term is missing X2 + 14x + ____ Find the constant term by squaring half the coefficient of the linear term. (14/2) X2 + 14x + 49

5
**Perfect Square Trinomials**

Create perfect square trinomials. x2 + 20x + ___ x2 - 4x + ___ x2 + 5x + ___ 100 4 25/4

6
**Solving Quadratic Equations by Completing the Square**

Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation

7
**Solving Quadratic Equations by Completing the Square**

Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

8
**Solving Quadratic Equations by Completing the Square**

Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

9
**Solving Quadratic Equations by Completing the Square**

Step 4: Take the square root of each side

10
**Solving Quadratic Equations by Completing the Square**

Step 5: Set up the two possibilities and solve

11
**Completing the Square-Example #2**

Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation, the constant to the right side of the equation.

12
**Solving Quadratic Equations by Completing the Square**

Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. The quadratic coefficient must be equal to 1 before you complete the square, so you must divide all terms by the quadratic coefficient first.

13
**Solving Quadratic Equations by Completing the Square**

Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

14
**Solving Quadratic Equations by Completing the Square**

Step 4: Take the square root of each side

15
**Example: Solve by completing the square. x2+6x-8=0**

Don’t forget: Whatever you add to one side of an equation, you MUST add to the other side!

16
**More Examples! 5x2-10x+30=0 x2-2x+6=0 x2-2x=-6 x2-2x+__=-6+__**

17
**Last Example. Write the quadratic function y=x2+6x+16 in vertex form**

Last Example! Write the quadratic function y=x2+6x+16 in vertex form. What is the vertex of the function’s graph? y=x2+6x+16 y-16=x2+6x y-16+__=x2+6x+__ y-16+9=x2+6x+9 y-7=(x+3)2 y=(x+3)2+7 If the equation, in vertex form, is y=(x+3)2+7, then the vertex must be (-3,7).

18
**Solving Quadratic Equations by Completing the Square**

Try the following examples. Do your work on your paper and then check your answers.

Similar presentations

© 2019 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