Quadratic Functions and Equations
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Questions and Answers

What are the zeros of the quadratic function 𝑓(𝑥) = 2𝑥^2 − 𝑥 − 3?

  • 𝑥 = 2 and 𝑥 = -1 (correct)
  • 𝑥 = 1 and 𝑥 = -2
  • 𝑥 = 3 and 𝑥 = -2
  • 𝑥 = -3 and 𝑥 = 1
  • For a Fitness Health Club, if the demand equation is 𝒒 = -0.06𝑝 + 84, what does 'p' represent in the equation?

  • Number of quantities produced
  • Price of a unit of goods produced
  • Annual membership fee (correct)
  • Total cost
  • What does the total cost function 𝑪(𝑄) = 𝒎𝑄 + 𝒃 represent?

  • Fixed cost (correct)
  • Variable cost
  • Number of quantities produced
  • Total revenue
  • In the context of quadratic functions, what does the total profit function 𝝅(𝑄) represent?

    <p>Total revenue minus total cost</p> Signup and view all the answers

    If the total revenue function is given by 𝑅(𝑄) = 𝑃𝑄, what does 'P' represent?

    <p>Price per unit of goods sold</p> Signup and view all the answers

    What are the turning points of the quadratic function 𝑓(𝑥) = 2𝑥^2 − 𝑥 − 3?

    <p>(4, -4)</p> Signup and view all the answers

    What is the equation of a quadratic function?

    <p>$f(x) = ax^2 + bx + c$</p> Signup and view all the answers

    When is a graph of a quadratic function concave?

    <p>When $a &lt; 0$</p> Signup and view all the answers

    What is the formula to find the value of $x$ at the maximum or minimum point of a quadratic function?

    <p>$x = -\frac{b}{2a}$</p> Signup and view all the answers

    Which method can be used to solve a quadratic equation?

    <p>Factorization</p> Signup and view all the answers

    For the equation $3Q^2 - 2Q + 1 = 0$, what is the correct way to find the solution?

    <p>Use factorization</p> Signup and view all the answers

    In drawing the graph of a quadratic function, what should you do after finding the $x$-intercepts?

    <p>Find the turning point</p> Signup and view all the answers

    What is the formula for annual revenue as a function of the membership price?

    <p>$-0.06p^2 + 84p$</p> Signup and view all the answers

    What is the formula for the annual cost function?

    <p>$-1.2p^2 + 84p$</p> Signup and view all the answers

    What does the profit function represent in this scenario?

    <p>Annual Revenue minus Annual Cost</p> Signup and view all the answers

    At what price should the annual membership fee be set to obtain maximum revenue?

    <p>$710$</p> Signup and view all the answers

    What is the maximum possible revenue that can be obtained?

    <p>GH¢29,400</p> Signup and view all the answers

    At what price should the annual membership fee be set to obtain maximum profit?

    <p>$700</p> Signup and view all the answers

    What is the formula for the cost of operating George's shop per day?

    <p>$2x^2 - 20x + 360$</p> Signup and view all the answers

    What does George need to find to minimize his shop's operating cost?

    <p>Number of sandwiches batches sold</p> Signup and view all the answers

    What is the minimum cost of operating George's shop per day?

    <p>$160</p> Signup and view all the answers

    What is the formula for the average daily cost per batch of sandwiches as a function of x?

    <p>$\frac{2x^2 - 20x + 360}{x}$</p> Signup and view all the answers

    What is the average daily cost per batch of sandwiches when 7 batches are produced?

    <p>$60</p> Signup and view all the answers

    For the first trial example, what is the total cost function if x products are demanded in a particular week?

    <p>14 + 3𝑥</p> Signup and view all the answers

    In the second trial example, what is the firm's total revenue function given a constant selling price of GH¢60?

    <p>60𝑥 - 450</p> Signup and view all the answers

    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?

    <p>25𝑥 - 485</p> Signup and view all the answers

    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.

    <p>TC(x) = 685x + 125,000</p> Signup and view all the answers

    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?

    <p>$x = 120$ units</p> Signup and view all the answers

    What is the maximum possible profit (in dollars) for Ms. Tilden's pie shop if the profit function is 𝑃(𝑥) = 120𝑥 − 𝑥?

    <p>$P_{max} = $7,200</p> Signup and view all the answers

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