I can find zeros by completing the square Warm Up Rewrite the following as perfect squares 1 x 2 14x 49 2 2 x 2 2x 1 2 Our goal What if you were asked to complete the pattern of a perfect square ID: 743703
Download Presentation The PPT/PDF document "Complete the Square Objective" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Complete the Square
Objective
I can find zeros by completing the squareSlide2
Warm Up
Rewrite the following as perfect squares.
1. x
2
+ 14x + 49
( _______)
2
2. x
2
-2x + 1
(________)
2Slide3
Our goal
What if you were asked to complete the pattern of a perfect square.
x
2
+ 20x + ____
( )2OYOx2 -18x + ______(_______)2
This Process is called “Completing the Square” because our goal is to figure out what number you need to create a perfect square.Slide4
Not So Perfect S
quares.
Some equations aren’t as easy to see what value will complete the square such as.
For these we use
(b/2)
2Look back at the previous complete the square problems, how does the constant term of the factored binomial relate to the middle term?What will be the factored form of this quadratic?x2 + 9x + Slide5
Check It Out!
Example 2c
Complete the square for the expression. Write the resulting expression as a binomial squared.
x
2
+ 3x +
Add.
Factor.
Find .
Check
Find the square of the binomial.Slide6
Why?
We can use completing the square for two things.
S
olve quadratics by means of the square root property.
Transform a function in standard form to vertex form.
For this unit we will focus on solving equations by completing the square.Slide7
You can complete the square to solve quadratic equations.Slide8
Solve the equation by completing the square.
x
2
=
12x - 20Slide9
Solve the equation by completing the square.
18
x +
3
x
2 = 45Slide10
Solve the equation by completing the square.
2
x
2
+ 8x
= 12Slide11
Solve the equation by completing the square.
5
x
2
+ 10x
– 7 = 0Slide12
OYO
3
x
2
– 24
x
= 27
Solve the equation by completing the square.