# Pre-Calculus 1 Today’s Agenda Today’s Objectives: Today’s Vocabulary:

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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

Solving Quadratic Equations by Completing the Square

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

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

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 + ___

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

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.

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.

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)

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

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)

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.

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.

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