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Published byGabriella Porter Modified over 3 years ago

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Parabola Conic section

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

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Standard Form y = ax 2 + bx + c The parabola will open down when the a value is negative. The parabola will open up when the a value is positive. y x The standard form of a quadratic function is a = positive a = negative

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

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

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Graphing with vertex Vertex = (__, __) xy (__, __) 0 –4–4 Formula in finding the vertex x = –b_ 2a y = substitute the value of x y = ax 2 + bx + c

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

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y x Graphing: y = ax 2 + c 4. y = x 2 – 2 Vertex = (0, –2) 5. y = x Vertex = (0, 2) y x

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Graphing: y = ax 2 + c 5. y = x Vertex = (0, 2) y x 6. y = –x Vertex = (0, 2) y x

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Comparing Parabola y x x - axis y - axis Green y = 5x 2 Purple y = ½x 2 Blue y = ¼ x 2 Smaller coefficient = Wider parabola

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