Modeling with Quadratic Equations

Question 1

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

To find the selling prices that generate a $50 profit, replace y with 50 in the equation: 50 = –10x² + 160x – 430. Next, rewrite the equation in standard form by subtracting 50 from both sides to get 0 = –10x² + 160x – 480. Factoring is the best method because the entire equation can be divided by –10 to get 0 = x² – 16x + 48, which easily factors into (x – 4)(x – 12) = 0. This results in selling prices of $4 or $12.

Question 2

Question 23

Revolt · Accepted Answer

-coordinate of the vertex of the function: D; -coordinate of the vertex of the function: B; an: C; a: A

Question 3

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

Revolt · Accepted Answer

✔ D; -coordinate of the vertex of the function: D; -coordinate of the vertex of the function: B; an: C; a: A

Question 4

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

Revolt · Accepted Answer

✔ y = 0.0025(x - 90)² + 6

Question 5

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

Revolt · Accepted Answer

26.25

Question 6

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

Revolt · Accepted Answer

180

Question 7

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

Revolt · Accepted Answer

✔ A(w) = -w² + 100w

Question 8

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

Revolt · Accepted Answer

PENDING

Question 9

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?

Revolt · Accepted Answer

If the soccer balls are too expensive, fewer will be sold, reducing profit.

Question 10

What is the vertex of the parbola? ([___], [___])

Revolt · Accepted Answer

7

Modeling with Quadratic Equations Answers

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