Typing hint: Type x2 as x^2 (shift 6 on the keyboard will give ^) 1) Solve the following quadratic equation by factoring: a) x 2 ? 6x ? 27 ? 0 b) Solve the quadratic equation 3?2 + 2x 16 = 0 using the quadratic formula. Read the information in the assignment list to learn more about how to type math symbols, such as the square root. ÿ 2) Use the graph of y = x2 + 4x 5 to answer the following: ÿ a) Without solving the equation or factoring, determine the solution(s) to the equation, x 2 ? 4x ? 5 ? 0 , using only the graph. ÿ Explain how you obtained your answer(s) by looking at the graph in a brief sentence: b) Does this function have a maximum or a minimum? Explain how you obtained your answer by looking at the graph in a brief sentence:: c) What are the coordinates of the vertex in (x, y) form? Answer: d) What is the equation of the line of symmetry for this parabola? Answer: ÿ ÿ ÿ ÿ 3) The profit function for Wannamaker Trophies is P(x) = -0.4?2 + fx m, where f represents the design fee for a customers awards and m represents the monthly office rent. Also, P represents the monthly profit in dollars of the small business where x is the number of awards designed in that month. a) If $80 is charged for a design fee, and the monthly studio rent is $1,600; write an equation for the profit, P, in terms of x. b) How much is the profit when 50 award designs are sold in a month? c) How many award designs must be sold in order to maximize the profit? Show your work algebraically. Trial and error is not an appropriate method of solution d) What is the maximum profit? 4) Graph the equation on the graph by completing the table and plotting the points. You may use Excel or another web-based graphing utility. a) y = x2 6x Use the values of x provided in the table to find the y values. x y 0 1 2 3 4 5 6
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