Quadratic Equations and Functions

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.

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,

x 2 ? 4x ? 5 ? 0 , using only the graph.

b) Does this function have a maximum or a minimum?

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) = -0.4×2 + 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

Answer:

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:

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

b) insert your graph here.