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The Graphs of Quadratic equations in completed square form Quadratic Equations

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Quadratics in completed square form The graphs of functions written in the form y = (x-a) 2 +b or y = b-(x-a) 2 are examined using the graphic calculator Introduction

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Quadratics in completed square form Press Y= and enter the function y = (x-4) 2 +2 in Y 1 Select FORMAT and choose GridOn Press ZOOM and select 6:ZStandard Press GRAPH

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Quadratics in completed square form The graph is that of a quadratic with a minimum at (4,2)

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Quadratics in completed square form Change the graph in Y 1 to read y = (x-6) 2 +1 Draw the graph again and note the minimum.

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Repeat the above procedure for each of the graphs shown noting the minimum for each graph. 1. y = (x-4) 2 + 2(4,2) 2. y = (x-6) 2 + 1 3. y = (x-5) 2 - 3 4. y = (x-2) 2 - 7 5. y = (x+4) 2 + 3 6. y = (x+1) 2 + 4 7. y = (x+6) 2 - 8 8. y = (x+3) 2 - 2 9. y = (x-7) 2 - 5 10. y = (x+2) 2 + 2 11. y = (x-5) 2 - 6 12. y = (x-4) 2 + 1 Equation of the quadratic Coordinates of the minimum

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Quadratics in completed square form Complete the statement The equation y = (x-a) 2 +b has a minimum at the point (, )

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Quadratics in completed square form Press Y= and enter the function y = 6 - (x-2) 2 in Y 1 Select FORMAT and choose GridOn Press ZOOM and select 6:ZStandard Press GRAPH

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The graph is that of a quadratic with a maximum at (2,6) Quadratics in completed square form

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Change the graph in Y 1 to read y = 3 - (x-5) 2 Draw the graph again and make a note of the maximum.

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Repeat the above procedure for each of the graphs shown noting the maximum for each graph. 1. y = 6 - (x-2) 2 (2,6) 2. y = 3 - (x-5) 2 3. y = 7 - (x-4) 2 4. y = 8 - (x+5) 2 5. y = 5 - (x+2) 2 6. y = -3 - (x-4) 2 7. y = -1 - (x-6) 2 8. y = -4 - (x+5) 2 9. y = -3 - (x+7) 2 10. y = 10 - (x-5) 2 11. y = 6 - (x+4) 2 12. y = -3 - (x-5) 2 Equation of the quadratic Coordinates of the maximum

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Complete the statement Quadratics in completed square form The equation y = b-(x-a) 2 has a maximum at the point (, )

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Quadratics in completed square form Consider the function y = 2(x-4) 2 +3. Enter this function in Y 1 and draw the graph. State the minimum Try different values for k, a and b in the formula y = k(x - a) 2 + b and use the graphs to help you to make a statement regarding the minimum value of functions of this form. Repeat the exercise for functions of the form y = b - k(x - a) 2

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