ip 2

new_first_part_of_unit_2_ip..docx

Students, you must submit your name and your chosen values for b and c in your quadratic function P(x) = -.2x^2 + bx – c from Problem 1 by Wednesday night or there will be a 10% deduction in your score for the Unit 2 Individual Project. This is part 3 in the directions.

I will start my own example using a similar quadratic function P(x) = -.1x^2 + bx – c. I will choose 90 as my b value and your b value must be a number between 100 and 200.

I will choose 4000 as my c value and your c value must be a number between 5000 and 10,000 based on the first letter in your last name and using the table provided in the directions.

My example function is P(x) = -.1x^2 + 90x – 4000. This is part 4 in the directions.

I will choose one value for x and it will be 300. You must choose five values for x and they must be between 500 and 1000.

I have P(300) = -.1*300^2 + 90*300 – 4000 and I calculate the exponent first. This gives P(300) = -.1*90,000 + 90*300 – 4000. Now I multiply and have P(300) = -9000 + 27,000 – 4000 and the final answer is P(300) = 14,000. Again you need to show work like this five times and get five P(x) values. This is for parts 5 and 6 in the directions.

You will then graph your quadratic function and the file in Learning Materials explains how to make a graph using Microsoft Excel and how to copy and paste the graph to your answer sheet. Your graph should be a parabola or a U-shaped curve.

In part 8 you need to find the vertex and you first use –b/2a to calculate another x value. I have a = -.1, b = 90, and c = -4000. You will have a = -.2 and different b and c values. I have –b/2a = -90/2*(-.1) which gives 90/.2 and then 450 as my x value. Then I calculate P(450) = -.1*450^2 + 90*450 – 4000. This gives P(450) = -.1*202500 + 90*450 – 4000 and then P(450) = -20,250 + 40500 – 4000 and finally P(450) = 16,250. The ordered pair for my vertex is (450, 16250).

I will let you find more about the equation of the line of symmetry by going to the reading assignment in our eBook for this week.

I will show how I rewrite my profit function in the form P(x) = a(x – h)^2 + k (This is part 10). I know my vertex is (450, 16250) from part 8. I also know that I have a = -.1 and since (h, k) represents the vertex, I have P(x) = -.1(x – 450)^2 + 16250. Remember you have a = -.2 in your profit function.

Be sure you complete all 14 parts of problem 1.