Objective: Prepare for Completing the Square by Reviewing Special Products, Square Roots

Date:______Page______

Objective: Prepare for Completing the Square By Reviewing Special products, square roots, radicals, and solving quadratics by finding square roots

Completing the Square notes 1/27/2009 1

Date:______Page______

Review solving by finding square roots

Tendency to want to multiply it out then factor!!!!

Review Special Products (Multiply and square binomials)

Practice: Square a binomial

Practice: Recognize a trinomial square

Practice: Make a trinomial square

What term should you add to so the result is a perfect square

X-Factor Game to review multiply, add

Completing the Square notes 1/27/2009 1

Date:______Page______

Objective: Solving by Completing the Square x2 + bx = c

Using the strategy – TRADITONAL TEXT

3) Student/peer problem
/ 1) Teacher Instruction
Algorithm / 2) Teacher example problem

/ 1) Write the original equation
Write the equation in the form
x2 + bx = c
It is critical to be able to identify b.
And to separate the constant. /

2) Find and /


/ 3) Add to each side of the equation:
You may want call the sum on the right side d for the algorithm.
Don’t just add , make sure you square it! /


Not:

4) Factor the left side (now a trinomial square) so it is written in the form:
d /
/ 5) Find the square root (of both sides)

What if is not a rational number? /
6)  Solve for x /
7)  Check Solution

Note: The extension to solving for ax2 + bx = c adds one step.

Summary:

Objective: Solving by Completing the Square ax2 + bx = c

Using the strategy – TRADITONAL TEXT

3) Student/peer problem
/ 1) Teacher Instruction
Algorithm / 2) Teacher example problem

1) Write the original equation
Write the equation in the form
ax2 + bx = c
It is critical to be able to identify b. /

/ 1a) Divide both sides of the equation to eliminate the leading coefficient, a.
Did this affect the solutions? /
2) Find and
Half of the middle term, then square it. / b=4; Note:

3) Add to each side of the equation:
You may want call the sum on the right side d for the algorithm. /

4) Factor the left side (now a trinomial square) so it is written in the form:
d /
5) Find the square root (of both sides)
/
What if is a rational number?
8)  Solve for x /
9)  Check Solution

Note: it is important to check solutions.

Summary:

Connections/Linkage

Have students sketch the graph and identify solutions.

Review what the graph should look like before sketching.

May need to review radicals, square roots, etc.

Do examples that give solutions like

Completing the Square notes 1/27/2009 2