quadratic equation solved by square root property
DESCRIPTION
Lesson 1 Grade 9 k to 12TRANSCRIPT
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Lesson 1: Illustrations of Quadratic Equations
Lesson 2: Solving Quadratic Equations
Extracting Square Roots Factoring Completing the square Using the Quadratic Formula
Lesson 3 : Nature of Roots of Quadratic Equations
Lesson 4: Sums and Product of the Roots of Quadratic Equations
Lesson 5: Equations Transformable to Quadratic Equations (Including Algebraic Equations)
Lesson 6 : Applications of Quadratic Equations and Rational Algebraic Equations
Lesson 7 : Quadratic Inequalities
1.Choose a leader2.Secretary3.2 Presenters
12 min11 min10 min9 min.8 min7 min6 min5 min4 min3 min2 min1 min1098765432210
1. How did you find the product?
2. In finding each product, what mathematics concepts or principles did you apply? Explain how you applied these mathematics concepts or principles?
3. How would you describe the products obtained?
4. Are the products polynomials? If YES, what common characteristics do these polynomials have?
1. How do you describe Linear equation?
2. How are these equations different from those which are linear?
3. What common characteristics do these equations have?
Activity1: Find My RootsDirections: Find the following square roots.
1.) 16
2. ) – 25
3.) 49
4.) – 64
5.) 121
6.) – 289
7.) 0.16
8.) ± 36
9.) 16 25
10.) ± 169 256
= 4
= –5
= 7
= –8
= 11
= – 17
= 0.4
= ± 6
= 4 5
± 13 = 16
Extracting Square RootsQuadratic equations that can be written in the form x2 = k ca be solve by applying the following properties:
1.) If k > 0, then x2 = k has two real solutions or roots: x = ± k 2.) If k = 0, then x2 = k has one real solutions or root: x = 03.) If k < 0, then x2 = k has no real solutions or roots: Examples:
x2 – 16 = 0x2 = 16x = ± 16x = ± 4
x2 + 10 = 10x2 = 10 – 10x2 = 0x = 0
x2 + 9 = 0x2 = –9no real roots
1.) x2 + 8x – 9
x x
Factors of – 9
9 ; -1-9 ; 1
Sum of factors8
-8
+ 9
– 1
OR x2
-9-x
9xx 9
x
-1( x + 9 ) ( x – 1 )
-3 ; 3
0
2.) 3x2 – x – 10
– 30x2
-30x2
=
factors Sum of factors-30x ; x
30x ; -x-15x ; 2x15x ; -2x-6x ; 5x6x ; -5x
-29x29x-13x13x-x x
3x2 – 6x + 5x – 10 (3x2 – 6x) + (5x – 10)3x(x – 2) + 5(x – 2)
OR
3x2
-105x
-6x
x -2
3x
5