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Parabola Conic section

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Quadratic Functions The graph of a quadratic function is a parabola. y x If the parabola opens up, the lowest point is called the vertex. Vertex If the parabola opens down, the vertex is the highest point. Vertex

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**Standard Form y = ax2 + bx + c**

The standard form of a quadratic function is y x a = negative a = positive y = ax2 + bx + c The parabola will open up when the a value is positive. The parabola will open down when the a value is negative.

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**Graph the quadratic equation by factoring**

Example Graph the quadratic equation by factoring y x 1. y = x2 + 2x - 15 (x - 3) ( x + 5) x = 3 , x =-5 Parabola opens upward

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**Example (x - 4) ( x - 2) x = 4 , x = 2 2. y = -(x2 - 6x + 8)**

Graph the quadratic equation by factoring 2. y = -(x2 - 6x + 8) y x (x - 4) ( x - 2) x = 4 , x = 2 Parabola opens downward

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**Graphing with vertex y = ax2 + bx + c Formula in finding the vertex**

y = substitute the value of x (__, __) –4 Vertex = (__, __) x y

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**Example Find the vertex of y = -3x2 + 6x + 5 y = -3x2 + 6x + 5**

Formula in finding the vertex x = –b_ 2a y = substitute the value of x Find the vertex of y = -3x2 + 6x + 5 x = –b_ 2a y = substitute the value of x y = -3x2 + 6x + 5 x = –6 2(-3) y = -3(1)2 + 6(1) + 5 x = –6 –6 y = y = 8 x = 1 Vertex = (1, 8)

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**Graphing: y = ax2 + c 4. y = x2 – 2 5. y = x2 + 2 Vertex = (0, –2)**

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**Graphing: y = ax2 + c 6. y = –x2 + 2 5. y = x2 + 2 Vertex = (0, 2)**

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**Smaller coefficient = Wider parabola**

Comparing Parabola y - axis y x Green y = 5x2 Purple y = ½x2 x - axis Blue y = ¼ x2 Smaller coefficient = Wider parabola

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And the Quadratic Equation……

And the Quadratic Equation……

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