1. Pre-Calculus 1 Today’s Agenda Today’s Objectives: Today’s Vocabulary:
a. HW #10 due – Simplifying Square Roots
b. Start Do Now
SWBAT…
Rewrite Standard form equations in Vertex form
Apply “complete the square” technique to Standard form equations
Understand that completing the square is another way to find solutions to quadratics
Notes:
Completing the Square
3. Classwork
4. Summary
Today’s Vocabulary:
Homework #11:
Pg 124 #
Square
Square root
Radical

2. Solving Quadratic Equations by Completing the Square

3. Perfect Square Trinomials
SWBAT…
Rewrite Standard form equations in Vertex form
Apply “complete the square” technique to Standard form equations
Understand that completing the square is another way to find solutions to quadratics
Perfect Square Trinomials
Examples
x2 + 6x + 9
x2 - 10x + 25
x2 + 12x + 36

4. Creating a Perfect Square Trinomial
SWBAT…
Rewrite Standard form equations in Vertex form
Apply “complete the square” technique to Standard form equations
Understand that completing the square is another way to find solutions to quadratics
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)2 = 72 = 49
X2 + 14x + 49

5. Perfect Square Trinomials
SWBAT…
Rewrite Standard form equations in Vertex form
Apply “complete the square” technique to Standard form equations
Understand that completing the square is another way to find solutions to quadratics
Perfect Square Trinomials
Create perfect square trinomials
x2 + 20x + ___
x2 - 4x + ___
x2 + 5x + ___

6. Solving Quadratic Equations by Completing the Square
SWBAT…
Rewrite Standard form equations in Vertex form
Apply “complete the square” technique to Standard form equations
Understand that completing the square is another way to find solutions to quadratics
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
SWBAT…
Rewrite Standard form equations in Vertex form
Apply “complete the square” technique to Standard form equations
Understand that completing the square is another way to find solutions to quadratics
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
SWBAT…
Rewrite Standard form equations in Vertex form
Apply “complete the square” technique to Standard form equations
Understand that completing the square is another way to find solutions to quadratics
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
SWBAT…
Rewrite Standard form equations in Vertex form
Apply “complete the square” technique to Standard form equations
Understand that completing the square is another way to find solutions to quadratics
Solving Quadratic Equations by Completing the Square
If you want the vertex form of the equation you are almost there:
(x-4)2 = 36 can be converted into vertex form by subtracting 36 from both sides.
So you get:
(x-4)2 – 36 = 0 with vertex (4, -36)

10. Solving Quadratic Equations by Completing the Square
SWBAT…
Rewrite Standard form equations in Vertex form
Apply “complete the square” technique to Standard form equations
Understand that completing the square is another way to find solutions to quadratics
Solving Quadratic Equations by Completing the Square
To find the roots of the equation:
Step 4: Take the square root of each side

11. Solving Quadratic Equations by Completing the Square
SWBAT…
Rewrite Standard form equations in Vertex form
Apply “complete the square” technique to Standard form equations
Understand that completing the square is another way to find solutions to quadratics
Solving Quadratic Equations by Completing the Square
Step 5: Set up the two possibilities and solve
So your two roots written as x-intercepts are: (-10, 0) and (2,0)

12. Completing the Square-Example #2
SWBAT…
Rewrite Standard form equations in Vertex form
Apply “complete the square” technique to Standard form equations
Understand that completing the square is another way to find solutions to quadratics
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.

13. Solving Quadratic Equations by Completing the Square
SWBAT…
Rewrite Standard form equations in Vertex form
Apply “complete the square” technique to Standard form equations
Understand that completing the square is another way to find solutions to quadratics
(x + 1)2 = 64
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.
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
SWBAT…
Rewrite Standard form equations in Vertex form
Apply “complete the square” technique to Standard form equations
Understand that completing the square is another way to find solutions to quadratics
Solving Quadratic Equations by Completing the Square
Try the following examples. Do your work on your paper and then check your answers.
x2 + 8x - 84 = 0
x2 – 5x - 24 = 0
x = 6, x = -14
x = -3, x = 8