Solve the following quadratic equation by factoring

Typing hint:  Type x2 as x^2 (shift 6 on the keyboard will give ^) 

1) Solve the following quadratic equation by factoring: 

a) 0 2762   xx 

Answers: Show your work here:   

b) Solve the quadratic equation 3x2 + 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. 

Answers: Show your work here:     

2)    Use the graph of y = x2 + 4x - 5 to answer the following:  

a) Without solving the equation or factoring, determine the solution(s) to the equation, 0 542   xx , using only the graph.   Answer: 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? 

Answer: 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:       

3) The profit function for Wannamaker Trophies is P(x) = -0.4x2 + fx - m,  where f represents the design fee for a customer’s 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. 

 Typing hint:  Type x-squared as x^2 

b) How much is the profit when 50 award designs are sold in a month?   Answer:   Show your work here:  

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 –  use methods taught in class.    Answer:   Show your work here:  

d) What is the maximum profit? 

 Answer:    Show your work here:    

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  

b) Place your graph here.