Modeling with Quadratic Equations

Question 1

Question 1

Revolt · Accepted Answer

A(w) = 50w – w2

Question 2

Question 2

Revolt · Accepted Answer

625

Question 3

Find the length and width of the greatest rectangular area that the farmer can enclose with 100 m of fencing. The length is m and the width is m.

Revolt · Accepted Answer

25; Selection 1: 25; Selection 2: 25

Question 4

Question 4

Revolt · Accepted Answer

25

Question 5

Choose the quadratic equation that models the situation.

Revolt · Accepted Answer

h(t) = -4.9t² + 60

Question 6

To the nearest tenth of a second, how long after the pebble falls will it hit the ground? s

Revolt · Accepted Answer

3.5

Question 7

What is the equation that describes the parabola formed by the arch?

Revolt · Accepted Answer

y = -0.071(x - 13)² + 12

Question 8

To the nearest foot, what is the width of the arch 8 ft above the water? ft

Revolt · Accepted Answer

15

Question 9

The quadratic function y = –10x2 + 160x – 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. What equation do you need to solve to find the selling price or prices that would generate $50 in daily profit? What method would you use to solve the equation? Justify your choice.

Revolt · Accepted Answer

Replace y with 50 to get 50 = -10x² + 160x - 430. In standard form, this becomes x² - 16x + 48 = 0, which factors as (x - 4)(x - 12) = 0. I would use factoring because the quadratic factors easily, giving selling prices of $4 and $12.

Question 10

Compare your response with the sample response included here. Did your explanation

Revolt · Accepted Answer

say to replace y with 50?; say that the equation should be in standard form?; include factoring as the solution method?

Modeling with Quadratic Equations Answers

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