Notes Day 6.5

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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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### Notes Day 6.5

Choose the Best Regression Equation

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.”

.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

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.