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Warm-Up Factor the following trinomials. What do you notice?

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Presentation on theme: "Warm-Up Factor the following trinomials. What do you notice?"— Presentation transcript:

1 Warm-Up Factor the following trinomials. What do you notice? 1. x2 - 6x x2 - 4x + 1

2 Completing the Square

3 Today’s Objective Today, you’ll learn how to solve equations by completing the square.

4 Perfect Square Trinomials
1) x2 – 8x + ____ ) x2 + 16x + ____ x2 + 7x + ____ ) x2 – 13x + ____

5 Can you write a formula that will work for every example?
1) x2 – 8x + ____ ) x2 + 16x + ____ x2 + 7x + ____ ) x2 – 13x + ____

6 This will always result in a perfect square trinomial!
Introducing… the magic number! This will always result in a perfect square trinomial!

7 Adding the magic number,
to both sides of a quadratic equation is called completing the square.

8 Example 1: Solve by Completing the Square
Solve x2 – 12x + 5 = 0. First: x2 – 12x + ____ = -5

9 Example 2: Solve by Completing the Square
Solve x2 – 8x + 36 = 0.

10 Example 3: Solve by Completing the Square
Solve 5x2 = 6x + 8.

11 Vertex Form

12 Standard form vertex

13 Vertex: highest or lowest
point on the graph. 2 ways to find Vertex: 1) Calculator: 2nd  CALC MIN or MAX 2) Algebraically

14 Find the Vertex x2 + 8x + 1 x2 + 2x – 5 2x2 – 10x + 3

15 Complete the Square Investigation
Step 1: Complete the square: X2 + 4x – 4 = 0 Step 2: DON’T SOLVE! Instead get zero on one side. Step 3: graph the non-zero side and find the vertex

16 Completing the Square Finds the vertex!
Use completing the square to find the vertex of each: x2 + 6x + 8 = 0 X2 – 2x + 10 = 0

17 Vertex Form Lucky for us, we can use a calculator to find the vertex instead of completing the square!

18 Converting from Standard to Vertex
Standard: y = ax2 + bx + c Things you will need: a = and Vertex: Vertex: y = a(x – h)2 + k

19 Example Convert from standard form to vertex form. y = -3x2 + 12x + 5

20 Example Convert from standard form to vertex form. y = x2 + 2x + 5

21 Now Convert and Solve Convert each quadratic from standard to vertex form. Then Solve for x. x2 + 6x – 5 = 0

22 Now Convert and Solve Convert each quadratic from standard to vertex form. 3x2 – 12x + 7 = 0 -2x2 + 4x – 3 = 0


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