2 Quadratic FunctionsThe graph of a quadratic function is a parabola.yxIf the parabola opens up, the lowest point is called the vertex.VertexIf the parabola opens down, the vertex is the highest point.Vertex
3 Standard Form y = ax2 + bx + c The standard form of a quadratic function isyxa = negativea = positivey = ax2 + bx + cThe parabola will open up when the a value is positive.The parabola will open down when the a value is negative.
4 Graph the quadratic equation by factoring ExampleGraph the quadratic equation by factoringyx1. y = x2 + 2x - 15(x - 3) ( x + 5)x = 3 , x =-5Parabola opens upward
5 Example (x - 4) ( x - 2) x = 4 , x = 2 2. y = -(x2 - 6x + 8) Graph the quadratic equation by factoring2. y = -(x2 - 6x + 8)yx(x - 4) ( x - 2)x = 4 , x = 2Parabola opens downward
6 Graphing with vertex y = ax2 + bx + c Formula in finding the vertex y = substitute the value of x(__, __)–4Vertex = (__, __)xy
7 Example Find the vertex of y = -3x2 + 6x + 5 y = -3x2 + 6x + 5 Formula in finding the vertexx = –b_2ay = substitute the value of xFind the vertex of y = -3x2 + 6x + 5x = –b_2ay = substitute the value of xy = -3x2 + 6x + 5x = –62(-3)y = -3(1)2 + 6(1) + 5x = –6–6y =y = 8x = 1Vertex = (1, 8)
8 Graphing: y = ax2 + c 4. y = x2 – 2 5. y = x2 + 2 Vertex = (0, –2)
9 Graphing: y = ax2 + c 6. y = –x2 + 2 5. y = x2 + 2 Vertex = (0, 2)
10 Smaller coefficient = Wider parabola Comparing Parabolay - axisyxGreen y = 5x2Purple y = ½x2x - axisBlue y = ¼ x2Smaller coefficient = Wider parabola
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