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Notes Day 6.5

Notes Day 6.5. Choose the Best R egression E quation Volume of a Box cubic Application Problems. Complete a regression equation to find the best model. Go to “catalog” on the calculator and turn “diagnostics on.”. Quadratic:. .9304. R 2 =. Y = -9.326x 2 + 109.571x – 20.288 . Cubic:. 1.

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Notes Day 6.5

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  1. Notes Day 6.5 Choose the Best Regression Equation Volume of a Box cubic Application Problems

  2. Complete a regression equation to find the best model. Go to “catalog” on the calculator and turn “diagnostics on.” Quadratic: .9304 R2= Y = -9.326x2 + 109.571x – 20.288 Cubic: 1 R2= Y = 5x3 – 9x2– (2.4• 10-11)x + 8 1 but not really quartic R2= Quartic: Y = (5.57• 10-12)x4 + 5x3– 9x2 + 8 Cubic Regression is best

  3. An open box is to be made from a 10-in. by 12-in. piece of cardboard by cutting x-inch squares in each corner and then folding up the sides. Write a function giving the volume of the box in terms of x. Approximate the value of x that produces the greatest volume. A. Label the side lengths in terms of x 12 – 2x Write an equation in factored form for the volume as if the box were closed. x x V(x)=(12 – 2x)(10 – 2x)(x) C. Find the roots and plot on the graph. 10 – 2x X = {6,5,0} Write the volume equation in standard form and plot the end behavior on the graph. V(x)=(120 – 44x + 4x2)(x) V(x)=4x3 – 44x2 + 120x 90 E. Find the relative min/max on the calculator. Plot. (1.811 , 96.771) Min(5.523 , - 5.511) F. Explain what this ordered pair represents? Cuts of 1.811 inches will maximize volume to 96.771 cubic inches 5 Why isn’t volume greatest as x approaches infinity? Some dimensions would be negative. G. What are the dimensions of the box? 8.378 in. by 6.378 in. by 1.811 in.

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