29 Questions
What are the zeros of the quadratic function 𝑓(𝑥) = 2𝑥^2 − 𝑥 − 3?
𝑥 = 2 and 𝑥 = -1
For a Fitness Health Club, if the demand equation is 𝒒 = -0.06𝑝 + 84, what does 'p' represent in the equation?
Annual membership fee
What does the total cost function 𝑪(𝑄) = 𝒎𝑄 + 𝒃 represent?
Fixed cost
In the context of quadratic functions, what does the total profit function 𝝅(𝑄) represent?
Total revenue minus total cost
If the total revenue function is given by 𝑅(𝑄) = 𝑃𝑄, what does 'P' represent?
Price per unit of goods sold
What are the turning points of the quadratic function 𝑓(𝑥) = 2𝑥^2 − 𝑥 − 3?
(4, -4)
What is the equation of a quadratic function?
$f(x) = ax^2 + bx + c$
When is a graph of a quadratic function concave?
When $a < 0$
What is the formula to find the value of $x$ at the maximum or minimum point of a quadratic function?
$x = -\frac{b}{2a}$
Which method can be used to solve a quadratic equation?
Factorization
For the equation $3Q^2 - 2Q + 1 = 0$, what is the correct way to find the solution?
Use factorization
In drawing the graph of a quadratic function, what should you do after finding the $x$-intercepts?
Find the turning point
What is the formula for annual revenue as a function of the membership price?
$-0.06p^2 + 84p$
What is the formula for the annual cost function?
$-1.2p^2 + 84p$
What does the profit function represent in this scenario?
Annual Revenue minus Annual Cost
At what price should the annual membership fee be set to obtain maximum revenue?
$710$
What is the maximum possible revenue that can be obtained?
GH¢29,400
At what price should the annual membership fee be set to obtain maximum profit?
$700
What is the formula for the cost of operating George's shop per day?
$2x^2 - 20x + 360$
What does George need to find to minimize his shop's operating cost?
Number of sandwiches batches sold
What is the minimum cost of operating George's shop per day?
$160
What is the formula for the average daily cost per batch of sandwiches as a function of x?
$\frac{2x^2 - 20x + 360}{x}$
What is the average daily cost per batch of sandwiches when 7 batches are produced?
$60
For the first trial example, what is the total cost function if x products are demanded in a particular week?
14 + 3𝑥
In the second trial example, what is the firm's total revenue function given a constant selling price of GH¢60?
60𝑥 - 450
In the second trial example, what is the profit function for the firm with a fixed cost of GH¢450 and variable cost of GH¢35?
25𝑥 - 485
Express the firm's total cost (TC) as a function of output (x) given a fixed cost of GH¢125,000 and variable cost of GH¢685 per item manufactured.
TC(x) = 685x + 125,000
In Ms. Tilden's pie shop scenario, how many units of pies must be sold to maximize profit if the profit function is given by 𝑃(𝑥) = 120𝑥 − 𝑥?
$x = 120$ units
What is the maximum possible profit (in dollars) for Ms. Tilden's pie shop if the profit function is 𝑃(𝑥) = 120𝑥 − 𝑥?
$P_{max} = $7,200
Learn about quadratic functions and equations, including their definitions, graphs, and how to find the maximum or minimum point of a quadratic function. Practice sketching the graphs of quadratic functions with given equations.
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