Download presentation
Presentation is loading. Please wait.
Published byRoy Mason Modified over 9 years ago
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
Similar presentations
© 2024 SlidePlayer.com Inc.
All rights reserved.