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# Quadratic Equation

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by

Tweet## Michelle Veriah

on 24 February 2013#### Transcript of Quadratic Equation

Introduction Completing The Square The Discriminant Linear Inequalities When a does not equal to zero,

The solution of ax + bx + c = 0 is given by: The standard form of a

quadratic equation is: The Zero-Product Principle:

If the product of 2 algebraic expressions is zero, then at least one of the factors equal to zero.

If AB = 0

Then A = 0 or B = 0 Quadratics For the quadratic equation ax + bx + c = 0

The completed square form is: The discriminant = b - 4ac Linear inequalities can be solved with 2 methods: The End There are 3 ways of solving

a quadratic equation: ax + bx + c = 0 2 a, b, c are constants

a does not equal to 0 (a) Factorization

(b) The Quadratic Formula

(c) Completing The Square Solving Quadratic Equations Factorization Example:

3x - 5x + 2 = 0

(3x - 2)(x - 1) = 0

3x - 2 = 0 or x - 1 = 0

x = 2/3 or x = 1 The Quadratic Formula 2 Example: 2 2 The Parabola: when y = a ( x - h ) + k

(h, k) is the vertex

If a>0, vertex is a minimum point

If a<0, vertex is a maximum point 2 When discriminant > 0, there are 2 real solutions

When discriminant = 0, there is 1 real solution

When discriminant < 0, there are no real solutions Graphical Method: Algebraic Method:

Full transcriptThe solution of ax + bx + c = 0 is given by: The standard form of a

quadratic equation is: The Zero-Product Principle:

If the product of 2 algebraic expressions is zero, then at least one of the factors equal to zero.

If AB = 0

Then A = 0 or B = 0 Quadratics For the quadratic equation ax + bx + c = 0

The completed square form is: The discriminant = b - 4ac Linear inequalities can be solved with 2 methods: The End There are 3 ways of solving

a quadratic equation: ax + bx + c = 0 2 a, b, c are constants

a does not equal to 0 (a) Factorization

(b) The Quadratic Formula

(c) Completing The Square Solving Quadratic Equations Factorization Example:

3x - 5x + 2 = 0

(3x - 2)(x - 1) = 0

3x - 2 = 0 or x - 1 = 0

x = 2/3 or x = 1 The Quadratic Formula 2 Example: 2 2 The Parabola: when y = a ( x - h ) + k

(h, k) is the vertex

If a>0, vertex is a minimum point

If a<0, vertex is a maximum point 2 When discriminant > 0, there are 2 real solutions

When discriminant = 0, there is 1 real solution

When discriminant < 0, there are no real solutions Graphical Method: Algebraic Method: