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Published bySharleen Martin Modified over 4 years ago

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Goal: Graph quadratic functions in different forms

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Find the product: (x + 6)(x + 3) (x – 5) 2 4(x + 5)(x – 5) Write y = x(8x + 12) + 5 in Standard form

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DefinitionSteps to Graphing y = a(x – h) 2 + k When a>0 the parabola opens up When a<0 the parabola opens down x = h Step 1:Draw the axis of symmetry. It is the line x = h. (h, k) Step 2: Plot the vertex (h, k) Step 3:Plot two points on one side of the axis of symmetry. Use symmetry to plot two more points on the opposite side of the axis of symmetry Step 4: Draw a parabola through the points

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DefinitionSteps for Graphing y = a(x – p)(x – q) When a < 0 the parabola opens down When a > 0 the parabola opens up The graph will contain (p, 0) and (q, 0) x = p + q Step 1: Draw the axis of symmetry. It is the line x = p + q 2 p + q Step 2: Find and plot the vertex. The x- coordinate of the vertex is p + q 2 Substitute the x-coordinate for x in the function to find the y-coordinate of the vertex. Step 3: Plot the points where the x- intercepts, p and q, occur. Step 4: Draw a parabola

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Minimum Value When a > 0 Maximum Value When a < 0

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Tell whether the function y = -4 (x + 6)(x – 4) has a minimum value or a maximum value. Then find the minimum or maximum value.

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Tell whether the function y = ½ (x + 8) 2 – 12 has a minimum value or a maximum value. Then find the minimum or maximum value.

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Tell whether the function y = 3(x – 4)(x – 7) has a minimum value or a maximum value. Then find the minimum or maximum value.

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