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Graphing Quadratics With VERTEX and Axis of Symmetry At the end of the period, you will learn: 1. To compare parabola by the coefficient 2. To find the vertex of a parabola

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Warm-up Graph the quadratic equation by factoring. Tell whether the quadratic opens upward or downward 1. y = - x 2 + 7x + 12 2. f(x)= x 2 + 21x + 20 3. y = - x 2 - 6x + 8

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Identifying Vertex f(x) = 2x - x 2 Vertex: (1,1)

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Identifying Vertex 4 Your turn! 4 f(x) = x 2 - 4 Vertex: (0, -4)

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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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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 –6–6 x = 1 y = substitute the value of x y = -3x 2 + 6x + 5 y = -3(1) 2 + 6(1) + 5 y = -3 + 6 + 5 y = 8 Vertex = (1, 8)

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Graph the Parabola y = -3x 2 + 6x + 5 Vertex = (1, 8) y x 2 4 6 8 1 2345

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

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Graph the Parabola y x 2 4 6 8 1 2345 y = x 2 + 2x – 5 Vertex = (-1, -6)

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Graphing Quadratics Review on graphing quadratics At the end of the period, you will master: 1. To graph parabola of this form: y = ax 2 + c

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Classwork Sketch the following parabola by finding the vertex 1. y = x 2 + 4x + 3 5. y = - x 2 + 4x - 4 2. y = –x 2 + 4x – 4 6. y = – x 2 + 8x – 5 4. y = x 2 - 10x + 20 3. y = x 2 + 3

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Warm-up Find the VERTEX and graph the PARABOLA 1. y = -3x 2 + 6x + 5 Vertex = (1, 8) 2. y = x 2 + 2x – 5 Vertex = (-1, -6) 3. y = x 2 + 4x – 5 Vertex = (-2,-9) 4. y = x 2 – 2 Vertex = (0, –2) Formula in finding the vertex x = –b_ 2a y = substitute the value of x

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

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

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Classwork Graph the following parabola using: I Finding the solution of the equations (Factoring) II Finding the VERTEX (Using formula) III Graphing on y-axis (using vertex) 1. y = - x 2 - 9x + 20 2. y = x 2 - 6x + 83. y = - x 2 - 7x + 10 3. y = x 2 + 6x - 81. y = x 2 + 4x + 32. y = –x 2 + 4x – 4 1. y = x 2 – 1 2. y = –x 2 + 2 3. y = x 2 - 5 4. y = –x 2 + 3

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