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Transcript of Quadratic Equation
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: