10 5 solving quadratic equations by completing the square
Download
1 / 14

10.5 Solving Quadratic Equations By Completing the Square - PowerPoint PPT Presentation


  • 88 Views
  • Uploaded on

10.5 Solving Quadratic Equations By Completing the Square. Review Square Root Method. Use if there is no linear term. (i.e. B = 0) Get the Quadratic Term on one side and the Constant on the other side. Simply take the Square Root of Both Sides. Square Root Method.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' 10.5 Solving Quadratic Equations By Completing the Square' - arlais


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
10 5 solving quadratic equations by completing the square

10.5 Solving Quadratic Equations By Completing the Square


Review square root method
Review Square Root Method

  • Use if there is no linear term. (i.e. B = 0)

  • Get the Quadratic Term on one side and the Constant on the other side.

  • Simply take the Square Root of Both Sides.


Square root method
Square Root Method

Be sure to give both the positive and negative answers!


Solving quadratic equations

Solving Quadratic Equations

by Completing the Square

Goal: Turn the problem into a Square Root Problem


Completing the square
Completing the Square

  • Take HALF the coefficient of the linear term (i.e. B ) and square.

  • Example: x2 + 8x + c

  • Example: x2 + 12x + c

  • Example: x2 + 9x + c

c = 16

c = 36

c = 81/4


Example 4 3a

Find the value of c that makes a perfect square. Then write the trinomial as a perfect square.

Step 1 Find one half of 16.

Step 2 Square the result of Step 1.

Step 3 Add the result of Step 2 to

Answer:The trinomial can be written as

Example 4-3a


Example 4 3b

Find the value of c that makes a perfect square. Then write the trinomial as a perfect square.

Example 4-3b

Answer: 9; (x + 3)2


Example 4 4a

Solve by completing the square.

Notice that is not a perfect square.

Rewrite so the left side is of the form

Since

add 4 to each side.

Write the left side as a perfect square by factoring.

Example 4-4a


Example 4 4a1

Square Root Property

Subtract 2 from each side.

Write as two equations.

or

Solve each equation.

Example 4-4a

Answer: The solution set is {–6, 2}.


Example 4 4b

Solve by completing the square.

Example 4-4b

Answer:{–6, 1}


Example 4 5a

Solve by completing the square.

Notice thatis not a perfect square.

Divide by the coefficient of the quadratic term, 3.

Add to each side.

Since

add to each side.

Example 4-5a


Example 4 5a1

Write the left side as a perfect square by factoring. Simplify the right side.

Square Root Property

Add to each side.

Example 4-5a


Example 4 5a2

Solve each equation.

Answer: The solution set is

Write as two equations.

or

Example 4-5a


Example 4 5b
Example 4-5b

Classwork/Homework


ad