{"text_format":"3","workbook":"xlsx","n_sheets":4,"sheets":["Pick a and b","Pick a and c","Pick b and c","Sheet2"],"not_rendered":{"charts":3,"images":9,"defined_names":13,"comments":3},"read":"whole","date_system":"1900"}

{"sheet":"Pick a and b","index":0,"n_rows":38,"n_cols":15,"rows_kept":38,"merged":[[31,2,31,3]]}
[null,"  Quadratic Rate of Growth"]
[]
[null,"This DIGMath module lets you investigate "]
[null,null,"  the rate of growth of"]
[null,"   quadratic functions y = ax2 + bx + c"]
[null,"   based on the coefficients a, b, and c."]
[]
[]
["What is the the value of  a (- 3 to 3)?",{"$nulls":3},{"$f":"H9/10-3","v":-0.7999999999999998},null,62,22]
[]
["What is the the value of  b (- 7 to 7)?",{"$nulls":3},{"$f":"I11/10 -7","v":3.4000000000000004},null,62,867,104]
[]
[]
[null,"The values for c are c = -10,  c = 0, and  c = 10."]
[]
[]
[null,"The interval used is from x = -4 to x = 4."]
[{"$nulls":9},"       Select the point of tangency x0 =",{"$nulls":3},{"$f":"-4+L20/10","v":-3.2}]
[]
[{"$nulls":11},8,{"$f":"a+L20*(b-a)/100","v":-3.36}]
[]
[]
["Click each item below for suggestions and investigations",{"$nulls":8},"At the point of tangency x0 =",null,null,{"$f":"x0","v":-3.2}]
[null,"   Item 1"]
[null,"   Item 2",{"$nulls":7},"   the slope of the tangent line when c = 10 is",{"$nulls":4},{"$f":"2*a0*x0+b0","v":{"v":8.52,"d":"8.520"}}]
[null,"   Item 3",{"$nulls":7},"   the slope of the tangent line when c = 0 is",{"$nulls":4},{"$f":"2*a0*x0+b0","v":{"v":8.52,"d":"8.520"}}]
[null,"   Item 4",{"$nulls":7},"   the slope of the tangent line when c = -10 is",{"$nulls":4},{"$f":"2*a0*x0+b0","v":{"v":8.52,"d":"8.520"}}]
[]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["     Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

{"sheet":"Pick a and c","index":1,"n_rows":38,"n_cols":15,"rows_kept":38,"merged":[[31,2,31,3]]}
[null,"   Quadratic Rate of Growth"]
[]
[null,"This DIGMath module lets you investigate "]
[null,null,"  the rate of growth of"]
[null,"   quadratic functions y = ax2 + bx + c"]
[null,"   based on the coefficients a, b, and c."]
[]
[]
["What is the the value of  a (- 3 to 3)?",{"$nulls":3},{"$f":"H9/10-3","v":-1.8},null,62,12]
[]
["What is the the value of  c (- 7 to 7)?",{"$nulls":3},{"$f":"H11/10 -7","v":1.4000000000000004},62,867,84]
[]
[]
[null,"The values for b are b = -2,  b = 2,  and  b = 6."]
[]
[]
[null,"The interval used is from x = - 4 to x = 4."]
[{"$nulls":9},"       Select the point of tangency x0 =",{"$nulls":3},{"$f":"-4+L20/10","v":0.2999999999999998}]
[]
[{"$nulls":11},43,{"$f":"a+L20*(b-a)/100","v":-0.56}]
[]
[]
["Click each item below for suggestions and investigations",{"$nulls":8},"At the point of tangency x0 =",null,null,{"$f":"x00","v":0.2999999999999998}]
[null,"   Item 1"]
[null,"   Item 2",{"$nulls":7},"   the slope of the tangent line when b = -2 is",{"$nulls":4},{"$f":"2*a00*x00-2","v":{"v":-3.079999999999999,"d":"-3.080"}}]
[null,"   Item 3",{"$nulls":7},"   the slope of the tangent line when b = 2 is",{"$nulls":4},{"$f":"2*a00*x00+2","v":{"v":0.9200000000000006,"d":"0.920"}}]
[null,"   Item 4",{"$nulls":7},"   the slope of the tangent line when b = 6 is",{"$nulls":4},{"$f":"2*a00*x00+6","v":{"v":4.920000000000001,"d":"4.920"}}]
[]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["     Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

{"sheet":"Pick b and c","index":2,"n_rows":38,"n_cols":15,"rows_kept":38,"merged":[[31,2,31,3]]}
[null,"  Quadratic Rate of Growth"]
[]
[null,"This DIGMath module lets you investigate "]
[null,null,"  the rate of growth of"]
[null,"   quadratic functions y = ax2 + bx + c"]
[null,"   based on the coefficients a, b, and c."]
[]
[]
["What is the the value of  b (- 3 to 3)?",{"$nulls":3},{"$f":"H9/10-3","v":0.3999999999999999},null,62,34]
[]
["What is the the value of  c (- 7 to 7)?",{"$nulls":3},{"$f":"H11/10 -7","v":-0.5},62,867,65]
[]
[]
[null,"The values for a are: a = -1,  a = 1,  and a = 3."]
[]
[]
[null,"The interval used is from x = -4 to x = 4."]
[{"$nulls":9},"     Select the point of tangency x0 =",{"$nulls":3},{"$f":"-4+L20/10","v":0.7000000000000002}]
[]
[{"$nulls":11},47,{"$f":"a+L20*(b-a)/100","v":-0.2400000000000002}]
[]
[]
["Click each item below for suggestions and investigations",{"$nulls":8},"At the point of tangency x0 =",null,null,{"$f":"x000","v":0.7000000000000002}]
[null,"   Item 1"]
[null,"   Item 2",{"$nulls":7},"   the slope of the tangent line when a = -1 is",{"$nulls":4},{"$f":"2*(-1)*x000+b000","v":{"v":-1.0000000000000004,"d":"-1.000"}}]
[null,"   Item 3",{"$nulls":7},"   the slope of the tangent line when a = 1 is",{"$nulls":4},{"$f":"2*(1)*x000+b000","v":{"v":1.8000000000000003,"d":"1.800"}}]
[null,"   Item 4",{"$nulls":7},"   the slope of the tangent line when a = 3 is",{"$nulls":4},{"$f":"2*(3)*x000+b000","v":{"v":4.600000000000001,"d":"4.600"}}]
[]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["     Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

{"sheet":"Sheet2","index":3,"n_rows":33,"n_cols":8,"rows_kept":33}
["a =",-4,null,"a =",-4,null,"a =",-4]
["b =",4,null,"b =",4,null,"b =",4]
[]
[{"$f":"x0","v":-3.2},{"$f":"a0*x0^2+b0*x0+10","v":-9.072000000000003},null,{"$f":"x00","v":0.2999999999999998},{"$f":"a00*x00^2+6*x00+c00","v":3.0379999999999994},null,{"$f":"x000","v":0.7000000000000002},{"$f":"-1*x000^2+b000*x000+c000","v":-0.7100000000000002}]
[]
["c = 10",null,null,"b=6",null,null,"a = -1"]
[{"$f":"a","v":-4},{"$f":"a0*A7^2+b0*A7+10","v":-16.4},null,{"$f":"a","v":-4},{"$f":"a00*D7^2+6*D7+c00","v":-51.4},null,{"$f":"a","v":-4},{"$f":"-1*G7^2+b000*G7+c000","v":-18.1}]
[0,{"$f":"a0*A8^2+b0*A8+10","v":10},null,0,{"$f":"a00*D8^2+6*D8+c00","v":1.4000000000000004},null,0,{"$f":"-1*G8^2+b000*G8+c000","v":-0.5}]
[{"$f":"b","v":4},{"$f":"a0*A9^2+b0*A9+10","v":10.800000000000004},null,{"$f":"b","v":4},{"$f":"a00*D9^2+6*D9+c00","v":-3.4000000000000004},null,{"$f":"b","v":4},{"$f":"-1*G9^2+b000*G9+c000","v":-14.9}]
[]
[{"$f":"x0","v":-3.2},{"$f":"a0*A11^2+b0*A11+10","v":-9.072000000000003},null,{"$f":"x00","v":0.2999999999999998},{"$f":"a00*D11^2+6*D11+c00","v":3.0379999999999994},null,{"$f":"x000","v":0.7000000000000002},{"$f":"-1*G11^2+b000*G11+c000","v":-0.7100000000000002}]
[{"$f":"x0+0.1","v":-3.1},{"$f":"a0*A12^2+b0*A12+10","v":-8.228000000000002},null,{"$f":"x00+0.1","v":0.3999999999999998},{"$f":"a00*D12^2+6*D12+c00","v":3.511999999999999},null,{"$f":"x000+0.1","v":0.8000000000000002},{"$f":"-1*G12^2+b000*G12+c000","v":-0.8200000000000003}]
[]
[]
["c = 0",null,null,"b=2",null,null,"a = 1"]
[{"$f":"a","v":-4},{"$f":"a0*A16^2+b0*A16+0","v":-26.4},null,{"$f":"a","v":-4},{"$f":"a00*D16^2+2*D16+c00","v":-35.4},null,{"$f":"a","v":-4},{"$f":"1*G16^2+b000*G16+c000","v":13.9}]
[0,{"$f":"a0*A17^2+b0*A17+0","v":0},null,0,{"$f":"a00*D17^2+2*D17+c00","v":1.4000000000000004},null,0,{"$f":"1*G17^2+b000*G17+c000","v":-0.5}]
[{"$f":"b","v":4},{"$f":"a0*A18^2+b0*A18+0","v":0.8000000000000043},null,{"$f":"b","v":4},{"$f":"a00*D18^2+2*D18+c00","v":-19.4},null,{"$f":"b","v":4},{"$f":"1*G18^2+b000*G18+c000","v":17.1}]
[]
[{"$f":"x0","v":-3.2},{"$f":"a0*A20^2+b0*A20+0","v":-19.072000000000003},null,{"$f":"x00","v":0.2999999999999998},{"$f":"a00*D20^2+2*D20+c00","v":1.838},null,{"$f":"x000","v":0.7000000000000002},{"$f":"1*G20^2+b000*G20+c000","v":0.27000000000000024}]
[{"$f":"x0+0.2","v":-3},{"$f":"a0*A21^2+b0*A21+0","v":-17.4},null,{"$f":"x00+0.2","v":0.49999999999999983},{"$f":"a00*D21^2+2*D21+c00","v":1.9500000000000002},null,{"$f":"x000+0.2","v":0.9000000000000001},{"$f":"1*G21^2+b000*G21+c000","v":0.6700000000000004}]
[]
[{"$f":"x0","v":-3.2},{"$f":"a0*A23^2+b0*A23+0","v":-19.072000000000003},null,{"$f":"x00","v":0.2999999999999998},{"$f":"a00*D23^2+2*D23+c00","v":1.838},null,{"$f":"x000","v":0.7000000000000002},{"$f":"1*G23^2+b000*G23+c000","v":0.27000000000000024}]
[]
["c = -10",null,null,"b = -2",null,null,"a = 3"]
[{"$f":"a","v":-4},{"$f":"a0*A26^2+b0*A26-10","v":-36.4},null,{"$f":"a","v":-4},{"$f":"a00*D26^2-2*D26+c00","v":-19.4},null,{"$f":"a","v":-4},{"$f":"3*G26^2+b000*G26+c000","v":45.9}]
[0,{"$f":"a0*A27^2+b0*A27-10","v":-10},null,0,{"$f":"a00*D27^2-2*D27+c00","v":1.4000000000000004},null,0,{"$f":"3*G27^2+b000*G27+c000","v":-0.5}]
[{"$f":"b","v":4},{"$f":"a0*A28^2+b0*A28-10","v":-9.199999999999996},null,{"$f":"b","v":4},{"$f":"a00*D28^2-2*D28+c00","v":-35.4},null,{"$f":"b","v":4},{"$f":"3*G28^2+b000*G28+c000","v":49.1}]
[]
[{"$f":"x0","v":-3.2},{"$f":"a0*A30^2+b0*A30-10","v":-29.072000000000003},null,{"$f":"x00","v":0.2999999999999998},{"$f":"a00*D30^2-2*D30+c00","v":0.6380000000000009},null,{"$f":"x000","v":0.7000000000000002},{"$f":"3*G30^2+b000*G30+c000","v":1.2500000000000009}]
[{"$f":"x0+0.2","v":-3},{"$f":"a0*A31^2+b0*A31-10","v":-27.4},null,{"$f":"x00+0.2","v":0.49999999999999983},{"$f":"a00*D31^2-2*D31+c00","v":-0.049999999999998934},null,{"$f":"x000+0.2","v":0.9000000000000001},{"$f":"3*G31^2+b000*G31+c000","v":2.2900000000000005}]
[]
[{"$f":"x0","v":-3.2},{"$f":"a0*A33^2+b0*A33-10","v":-29.072000000000003},null,{"$f":"x00","v":0.2999999999999998},{"$f":"a00*D33^2-2*D33+c00","v":0.6380000000000009},null,{"$f":"x000","v":0.7000000000000002},{"$f":"3*G33^2+b000*G33+c000","v":1.2500000000000009}]