Quadratic Functions and Equations in Financial Context — Quiz Answers

To determine whether a company’s profits will justify purchasing its stock, an investor wants to know the maximum possible profits for the company's signature product. The profit formula for the signature product can be represented using the function P⁡(x)=−7⁢x^2+4,200⁢x−20,000 , where x is the selling price of the product. What numbers for the selling price and the projected profit at the maximum of the function can the investor use to determine whether purchasing the stock is viable? Round to the nearest cent if necessary. Enter your answer in the boxes.

An investor has $⁢30,000 to distribute between two investments. The risk function is R⁡(x)=0.035⁢x^2−0.022⁢x+0.011 , where x is the portion invested in the first option. How much should the investor put into the second option to minimize risk? Round to the nearest hundredth if necessary.

To determine whether to purchase a company's stock, an investor will use a profit-prediction formula for a company's signature product depending on that product’s current selling price. The profit formula for the company can be represented using the function P⁡(x)=−20⁢x^2+4,400⁢x−24,000 , where x is the selling price of the product. Use a graphing calculator to determine the selling price that results in the maximum profits. Round to the nearest cent if necessary.

The price that companies set for a product is determined by market demand. The graph d⁡(x)=−0.036⁢x^2−0.09⁢x+6,000 represents the demand, where x is the number of units. Expand Image Which statement is true about the solution in terms of the situation? Round to the nearest whole number.

A shares transaction summary shows a total purchase price of $⁢8,743.80 before fees. If the share price had been $⁢0.20 cheaper, the investor could have purchased 35 more shares. Simplify the equation (8,743.50)/(x−0.2)−(8,734.8)/(x)=35 and use the quadratic formula to find the price per share of the stock. Round to the nearest hundredth if necessary.

The price that companies set for a product is determined by market demand. The graph d⁡(x)=−0.036⁢x^2−0.09⁢x+6,000 represents the demand, where x is the number of units. Expand Image Which statement is true about the solution in terms of the situation? Round to the nearest whole number.

For a new product that will be released nationwide, the revenue function is R⁡(x)=−0.007⁢x^2+18,125⁢x and the cost function is C⁡(x)=428,000+13,532⁢x In both functions, x is the number of units produced. How many units does the company need to sell to break even? Round your answer to the nearest thousand.

To anticipate future returns on earnings, a business owner starts by finding the break-even point of a new product. The revenue function is R⁡(x)=−0.0045⁢x^2+200⁢x , and the cost function is C⁡(x)=155,000+120⁢x In both functions, x is the number of units sold. According to the functions, what is the larger number of units the company can sell to break even? Round your answer to the nearest thousand. Enter your answer in the box.

An investor has $⁢60,000 to distribute between two investments. Let x be the portion invested in the first option. How much should the investor put into the first investment option to minimize risk if the risk function is R⁡(x)=0.019⁢x^2−0.034⁢x+0.017 ? Round your answer to the nearest hundred. Enter your answer in the box.

In the graph of the risk function for two investments R⁡(x) , x is the portion invested in the first of two options. What portion of the investment should the investor put into the first option? Round to the nearest hundredth. Expand Image Enter your answer in the box.

An investor is trying to minimize risk when distributing funds between two investments. The risk function is R⁡(x)=0.0802⁢x^2−0.0722⁢x+0.0361 If x is the portion invested in the first option, how should the investor distribute the funds to minimize risk?

In the graph of the risk function for two investments R⁡(x) , x is the portion invested in the first of two options. What portion of the investment should the investor put into the first option? Round to the nearest hundredth. Expand Image Enter your answer in the box.

The revenue function for a new tech gadget is R⁡(x)=−0.051⁢x^2+679⁢x The table shows various costs depending on the number of units produced. Units Cost ( $ ) 1,000 930,000 5,000 2,210,000 Write the linear cost function so that x is the number of units produced. What is the larger number of units that need to be sold to break even? Round your answer to the nearest whole number.

The price that companies set for a product is determined by market demand. The equation graph, where x is the number of units, represents the demand. For how many units is the demand 0 ? Round to the nearest whole number. Expand Image Enter your answer in the box.

The revenue function for a new tech gadget is R⁡(x)=−0.051⁢x^2+679⁢x The table shows various costs depending on the number of units produced. Units Cost ( $ ) 1,000 930,000 5,000 2,210,000 Write the linear cost function so that x is the number of units produced. What is the larger number of units that need to be sold to break even? Round your answer to the nearest whole number.

An investor wants to minimize risk by distributing funds into two options. The risk function is R⁡(x)=0.061⁢x^2−1.058⁢x+0.529 If x is the portion invested in the first option, how should the investor distribute the funds to minimize risk?