The early bird gets the worm, but the second mouse gets the cheese.

FST Section 9.1

 Write the general polynomial equation from the reading for today.

 What are the polynomial equations/functions you have already seen/studied in the past? Do they fit into the pattern found in the above general polynomial equation? How?

 Find the surface area and the volume of a box with one edge of unknown length, a second edge of one unit longer, and a third edge one unit shorter.

 Worksheet  Similar types of problems (categories)  Techniques  Mile Project  Data analysis (objective)  Data analysis (subjective)

 Find the outer surface area and the volume of an open box with one edge of unknown length, a second edge of one unit longer, and a third edge one unit shorter.  Hint: draw a picture  Hint: write as a polynomial function

 The general form for a polynomial in x is: n: degree of the polynomial a: the coefficients a n : leading coefficient The leading coefficient MUST be attached to the variable with the HIGHEST degree!

 Degree of polynomial  General shape  Even or odd function  End behavior  Number of possible “solutions” (x-intercepts)  Always one y-intercept  Number/location of possible Maximum points and minimum points ▪ Absolute versus relative (global versus local)

 Analysis:  y = a n x n format  Degree = n ▪ Odd or even? (only odd or only even terms) ▪ End behavior ▪ Max. number of possible x-intercepts ▪ Absolute versus local mins/maxes ▪ other

 A company has pieces of cardboard that are 60 cm by 80 cm. They want to make boxes from them (without a top) to hold equipment. Squares with sides of length x are cut from each corner and the resulting flaps are folded to make an open box.

 What’s the (max? min?) volume of the box that can be created?  Draw a picture to help!!

 Look at our answer for the cardboard box:  What’s the degree of the polynomial?  What’s the leading coefficient?  To standardize, we ALWAYS want to write polynomials in standard form (terms in order of descending degree)

 Use the volume formula we got from the cardboard box.  Find V(10)  What does this mean/represent?

 Monomial: a polynomial with one term  Binomial: a polynomial with two terms  Trinomial: a polynomial with three terms  Polynomial: general term for any polynomial (especially if it has more than three terms)

 Polynomials may have more than one variable  For example: x 2 y 3 – 3y 2 + 2x 2 – 6 This would be a polynomial in x and y  The degree of a polynomial in more than one variable is the largest sum of the exponents of the variables in any term.  In the example above, the degree is 5.

 Express the surface area and the volume of a cube with sides of length (a+b) in terms of a and b.  State the degree of each polynomial.

 Tamara is saving her summer earnings for college. The table shows the amount of money saved each summer.  At the end of each summer, she put her money in a savings account with an annual yield of 7%. How much will be in her account when she goes to college, if no additional money is added or withdrawn, and the interest rate remains constant? After Grade Amount Saved 8$600 9$900 10$ $ $1600

 At the end of each summer, she put her money in a savings account with an annual yield of 7%. How much will be in her account when she goes to college, if no additional money is added or withdrawn, and the interest rate remains constant?  Can you come up with a polynomial model?? (hint: start with an “exponential concept”) After Grade Amount Saved 8$600 9$900 10$ $ $1600

 Page : # 1 – 6, 9 – 12, 16  Define the following terms: functionlinear model independent variableexponential model dependent variablequadratic model mathematical model  Provide two examples of functions you use or see in everyday life. Describe the independent and dependent variables and how the functions are used.