Name: College ID: Thomas Edison State College College Algebra (MAT-121-GS) Section no.: Semester and year: Written Assignment 7 Answer all assigned exercises, and show all work. An asterisk indicates an exercise for which a graph pool is provided in the assignment submission link. 1. Given an equation and the graph of a quadratic function, do each of the following. (See section 3.1, Examples 1-4.) [4 points] a. Give the domain and range. b. Give the coordinates of the vertex. c. Give the equation of the axis. d. Find the y-intercept. e. Find the x-intercepts. 2. Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. Then determine (e) the interval of the domain for which the function is increasing and (f) the interval for which the function is decreasing. (See section 3.1, Examples 1-4.) [8 points] a. b. WA 7, p. 1 f ( x) 3( x 2)2 1 f ( x) 3x 2 24 x 46 3. Accident rateAccording to data from the National Highway Traffic Safety Administration, the accident rate as a function of the age of the driver in years x can be approximated by the function f ( x) 0.0232 x2 2.28x 60.0, for Find both the age at which the accident rate is a minimum and the 16 x 85. minimum rate. [4 points] 4. Use synthetic division to perform each division. (See section 3.2, Example 1.) [8 points] a. b. x 3 7 x 2 13 x 6 x2 x 4 x 3 5 x 2 3x x 1 5. Express f(x) in the form f ( x ) ( x k )q ( x ) r for the given value of k. [4 points] f ( x) 2 x3 3x 2 16 x 10; k 4 6. For each polynomial function, use the remainder theorem and synthetic division to find f(k). (See section 3.2, Example 2.) [8 points] a. b. WA 7, p. 2 f ( x) x 2 4 x 5; k 5 f ( x) x4 6 x3 9 x 2 3x 3; k 4 7. Use synthetic division to decide whether the given number k is a zero of the given polynomial function. If not, give the value of f(k). (See section 3.2, Examples 2 and 3.) [4 points] f ( x) 2 x3 9 x 2 16 x 12; k 1 8. Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first. (See section 3.3, Example 1.) [4 points] 2 x3 x 2; x 1 9. Factor f(x) into linear factors given that k is a zero of f(x). (See section 3.3, Example 2.) [4 points] f ( x) 2 x3 3x 2 5x 6; k 1 10. For the polynomial function, one zero is given. Find all others. (See section 3.3, Examples 2 and 6.) [4 points] f ( x) x3 4 x2 5; 1 11. For the polynomial function, find all zeros and their multiplicities. [4 points] f ( x) ( x 1)2 ( x 1)3 ( x2 10) 12. Find a polynomial function f(x) of degree 3 with real coefficients that satisfies the given conditions. (See section 3.3, Example 4.) [4 points] Zeros of 2, 3 and 5; f (3) 6 13. Find a polynomial function f(x) of least degree having real coefficients with zeros as given. (See section 3.3, Examples 4-6.) [4 points] WA 7, p. 3 7 2i and 7 2i 14. Sketch the graph of each polynomial function.* Determine the intervals of the domain for which each function is (a) increasing or (b) decreasing. (See section 3.4, Example 1.) [8 points] a. b. 5 f ( x) x5 4 1 f ( x) ( x 3) 4 3 3 15. Graph the polynomial function.* Factor first if the expression is not in factored form. (See section 3.4, Examples 3 and 4.) [4 points] f ( x) x( x 1)( x 1) 16. Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. (See section 3.4, Example 5.) [4 points] f ( x) 3x 2 x 4; 1 and 2 17. Show that the real zeros of the polynomial function satisfy the given conditions. (See section 3.4, Example 6.) [4 points] f ( x) 2x x 2 x 2 x 4 x 4; 5 4 3 2 no real zero greater than 1 18. Solve the following variation problem. (See section 3.6, Examples 1-4.) [4 points] If m varies jointly as z and p, and m = 10 when z = 2 and p = 7.5, find m when z = 6 and p = 9. WA 7, p. 4 19. Current in a circuitThe current in a simple electrical circuit varies inversely as the resistance. If the current is 50 amps when the resistance is 10 ohms, find the current if the resistance is 5 ohms. (See section 3.6, Examples 1-4.) [4 points] 20. Long-distance phone callsThe number of long-distance phone calls between two cities in a certain time period varies directly as the populations p1 and p2 of the cities and inversely as the distance between them. If 10,000 calls are made between two cities 500 mi apart, having populations of 50,000 and 125,000, find the number of calls between two cities 800 mi apart, having populations of 20,000 and 80,000. (See section 3.6, Examples 1-4.) [4 points] 21. Suppose y is inversely proportional to x, and x is tripled. What happens to y? [4 points] WA 7, p. 5