P2 Have a cover page, table of contents, and cite all sources. The average slope formula is: f(x2) - f(x1) / x2 - x1 It tells us the average slope over the interval from x1 to x2. Take the average...

P2 Have a cover page, table of contents, and cite all sources. The average slope formula is: f(x2) - f(x1) / x2 - x1 It tells us the average slope over the interval from x1 to x2. Take the average slope of the function x^2 + 3x +1 over one unit intervals from 0 to 10. Repeat for 2x^2 -2x +5. Graph the numbers (slopes), and what type of function do you see? Argue that the slope of a quadratic is a function that is independent of the constant term of the equation (“c“). Argue that a sum of linearly increasing integers will be approximately (or exactly!) quadratic.


P2 Have a cover page, table of contents, and cite all sources. The average slope formula is: f(x2) - f(x1) / x2 - x1 It tells us the average slope over the interval from x1 to x2. Take the average slope of the function x^2 + 3x +1 over one unit intervals from 0 to 10. Repeat for 2x^2 -2x +5. Graph the numbers (slopes), and what type of function do you see? Argue that the slope of a quadratic is a function that is independent of the constant term of the equation (“c“). Argue that a sum of linearly increasing integers will be approximately (or exactly!) quadratic. Each unit of brand awareness of a product generated by an ad campaign costs $.10 more than the previous one (I.e., the first costs .1, the second costs .1 more and is .2, the third costs .1 more, and is .3, etc.), and the overhead cost of $50 is needed to begin the ad campaign. Each unit of awareness generates exactly $5 in revenue. Find a function that models this in terms of awareness and profit. Graph it. How much awareness gets us to break even? How much maximizes the profit?