Modeling with Quadratic Equations Answers

Which quadratic equation models the situation correctly?

The main cable attaches to the left bridge support at a height of ft.

The main cable attaches to the right bridge support at the same height as it attaches to the left bridge support. What is the distance between the supports? ft

Which quadratic equation gives the area A of the rectangle in square feet given its width in w feet?

Determine the value of f, rounded to the nearest hundredth. ⇒ 0.39

Choose the quadratic model for the situation.

The main cable of a suspension bridge forms a parabola, described by the equation y = a(x − h)2 + k. y = height in feet of the cable above the roadway x = horizontal distance in feet from the left bridge support a = a constant (h, k) = vertex of the parbola What is the vertex of the parbola? (, )

Which quadratic equation models the situation correctly?

Complete the quadratic equation that models the situation. h(t) = –16t2 + ⇒ 24t + 6

A(w) = w2 – 50wA(w) = w2 – 100wA(w) = 50w – w2A(w) = 100w – w2

⇒ 625

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

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

Choose the quadratic equation that models the situation.h(t) = -4.9t² + 50.2h(t) = -4.9t² + 55.1✔ h(t) = -4.9t² + 60h(t) = -4.9t² + 66

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

What is the equation that describes the parabola formed by the arch?y = -0.090(x - 13)² + 12y = -0.090(x - 12)² + 13✔ y = -0.071(x - 13)² + 12y = -0.071(x - 12)² + 13

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

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.

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

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Match each item with what it represents in this situation by entering the appropriate letter in each box.ABC✔ D x-coordinate of the vertex of the function

Which quadratic equation models the situation correctly? y = -0.0025(x - 90)² + 6y = -0.0025(x - 30)² + 15✔ y = 0.0025(x - 90)² + 6y = 0.0025(x - 30)² + 15

The main cable attaches to the left bridge support at a height of ft.

The main cable attaches to the right bridge support at the same height as it attaches to the left bridge support. What is the distance between the supports? ft

Which quadratic equation gives the area A of the rectangle in square feet given its width in w feet?A(w) = -w² + 200w✔ A(w) = -w² + 100wA(w) = w² + 40wA(w) = w² + 90w

The rancher decides to make the width of the rectangle 40 ft. What is the area of the rectangle? ⇒ 2400 ft2

A sporting goods store uses quadratic equations to monitor the daily cost and profit for various items it sells. The store’s daily profit, y, when soccer balls are sold at x dollars each, is modeled by . Why is there an interval over which the graph decreases?

The rancher decides to make the width of the rectangle 40 ft. What is the area of the rectangle? ft2

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10✔ 2550

A✔ BCD y-coordinate of the vertex of the function

AB✔ CD an x-intercept of the function

✔ ABCD a y-intercept of the function