Section 3.3&3.4

9- For the quadratic function f(x) = x2 + 6x + 9, answer parts (a) through (f). (a) Find the vertex and the axis of symmetry of the quadratic function, and determine whether the graph is concave up or concave down. The vertex is |:|. (Type an ordered pair, using integers or fractions.) What is the equation of the axis of symmetry? The axis of symmetry is |:|. (Use integers or fractions for any numbers in the equation.) Is the graph concave up or concave down? 0 Concave down 0 Concave up (b) Find the y-intercept and the xintercepts, if any. Select the correct choice below and, if necessary, ll in the answer box to complete your choice. 0 A. The x-intercept(s) isfare |:|. (Type an integer or a simplied fraction. Use a comma to separate answers as needed.) 0 B. There are no x-intercepts. What is the y-intercept? Select the correct choice below and, if necessary, ll in the answer box to complete your choice. 0 A. The y-intercept is |:|. (Type an integer or a simplied fraction.) 0 B. There is no yintercept. (c) Use parts (a) and (b) to graph the function. Use the graphing tool to graph the function. (d) Find the domain and the range of the quadratic function. The domain of f is |:|. (Type your answer in interval notation.) The range off is |:|. (Type your answer in interval notation.) (e) Determine where the quadratic function is increasing and where it is decreasing. The function is increasing on the interval |:|. (Type your answer in interval notation.) The function is decreasing on the interval |:|. (Type your answer in interval notation.) (f) Determine where f(x) > O and where f(x) O on |:| and f(x) is never negative 0 3- f(x) Oon |:|andf(x) 0 and where f(x) 00n |:|andf(x) O on |:| and f(x) is never negative 1'1. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then nd the value. f(x)= 3x2 +18): 4 Does the quadratic function f have a minimum value or a maximum value? O The function f has a minimum value. 0 The function f has a maximum value. What is this minimum or maximum value? |:| (Simplify your answer.) 12_ The marginal cost of a product can be thought of as the cost of producing one additional unit of output. For example. if the marginal cost of producing the 50th product is $6.20. it cost $6.20 to increase production from 49 to 50 units of output. Suppose the marginal cost C (in dollars) to produce x thousand mp3 players is given by the function 000 = x2 140): + 8900. A. How many players should be produced to minimize the marginal cost? B. What is the minimum marginal cost? A. To minimize the marginal cost. |:| thousand mp3 players should be produced. B. The minimum marginal cost is $|:|. 13- The monthly revenue R achieved by selling x wristwatches is gured to be R(x) = Tlx 0.2xz. The monthly cost C of selling x wristwatches is 00:) = 28x +1650. (a) How many wristwatches must the rm sell to maximize revenue? What is the maximum revenue? (b) Prot is given as P(x) = R(x) C(x). What is the prot function? (c) How many wristwatches must the rm sell to maximize prot? What is the maximum prot? (d) Provide a reasonable explanation as to why the answers found in parts (a) and (c) differ. Explain why a quadratic function is a reasonable model for revenue. (a) The rm must sell |:| wristwatches to maximize revenue. (Round to the nearest integer as needed.) The maximum revenue is $|:|. (Round to two decimal places as needed.) (b) The prot function is P(x) = |:|. (Type an expression using x as the variable.) (c) The rm must sell |:| wristwatches to maximize prot. (Round to the nearest integer as needed.) The maximum profit is $|:|. (Round to two decimal places as needed.) (d) Why do the answer found in part (a) and part (c) differ? Choose the correct answer below. O A. The parts differ because part (3) uses the prot function which is equal to the difference of the revenue function and the cost function. 0 B. The parts differ because part (a) uses the revenue function which is equal to the sum of the prot function and the cost function. 0 C. The parts differ because part (c) uses the prot function which is equal to the product of the revenue function and the cost function. 0 D. The parts differ because part (c) uses the revenue function which is equal to the sum of the prot function and the cost function. Explain why a quadratic function is a reasonable model for revenue. Choose the correct answer below. 0 A. Revenue is the prot of the item plus the number x of units actually sold. So the revenue. R, is a quadratic function of the price p. O B. Revenue is the prot of the item times the numberx of units actually sold. So the revenue. R, is a quadratic function of the price p. O C. Revenue is the selling price of the item plus the number x of units actually sold. So the revenue, R, is a quadratic function of the price p. O D. Revenue is the selling price of the item times the number x of units actually sold. So the revenue. R, is a quadratic function of the price p. 14. David has available 400 yards of fencing and wishes to enclose a rectangular area. (3) Express the area Act the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area? (3) W) = |:| (b) The area is largest for W = |:| yards. (Simplify your answer.) (c) The maximum area is |:| square yards. (Simplify your answer.) 15. A suspension bridge with weight uniformly distributed along its length has twin towers that extend 85 meters above the road surface and are 1200 meters apart. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cables at a point 300 meters from the center. (Assume that the road is level.) The height of the cables is |:| meters. (Simplify your answer.) 16. A rain gutter is to be made of aluminum sheets that are 12 inches wide by turning up the edges 90. See the illustration. (a) What depth will provide maximum cross-sectional area and hence allow the most water to ow? (b) What depths will allow at least 16 square inches of water to ow? (a) The depth that will provide the maximum crosssectional area is |:| inches. (b) The depths between |:| in. and |:| in. will allow at least 15 square inches of water to ow