Quiz19solutions

# Quiz19solutions - MAC1105 Quiz#19 Solutions In the...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MAC1105: Quiz #19 Solutions July 26, 2010 In the top-right corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back. 1. Consider the quadratic function q(x) = (x - 3)2 - 4 (a) What is the vertex? h = 3; k = -4, so the vertex is (3, -4) (b) Does the graph open upwards or downwards? Upwards. (c) Find the x-intercepts, if any. 0 = (x - 3)2 - 4 (x - 3)2 = 4 x - 3 = 2 x = 5, 1 (d) Find the y -intercepts, if any. (0 - 3)2 - 4 = (-3)2 - 4 = 9 - 4 = 5 (e) Sketch the graph. 2. Write the following quadratic functions in standard form and state the vertex (Hint: a(x - h)2 + k): (a) q(x) = x2 - 3x + 2 3 q(x) = (x2 - 3x) + 2 = (x2 - 3x + 9 ) + 2 - 9 = (x - 2 )2 - 1 . Vertex: 4 4 4 3 1 (2, -4) 9 p(x) = (3x2 - 9x) - 6 = 3(x2 - 3x) - 6 = 3(x2 - 3x + 4 ) - 6 - 3 2 51 3 51 3(x - 2 ) - 4 . Vertex: ( 2 , 4 ) 27 4 (b) p(x) = 3x2 - 9x - 6 = 3. Suppose a soft-drink company determines that the price of a new zero1 calorie beverage obeys the demand equation p(x) = - 25 x + 100, where p is in cents. Find the price the company should set to maximize its revenue. We will complete the square to obtain an equation for the revenue, but in fact it is not necessary to nish nding the function in order to answer the question. Letting R(x) represent the revenue: 1 1 1 R(x) = p(x) x = - 25 x2 + 100x = - 25 (x2 - 2500x) == - 25 (x2 - 2500x + 12502 1 12502 2 2 1250 ) + 25 = - 25 (x - 1250) + 25 . 1 The only thing we need from this expression is the 1250, since that's the x coordinate of the vertex, i.e., the number of drinks sold to maximize the revenue. Plugging x = 1250 into the demand equation, we have: p(1250) = - 1 1250 + 100 = 50 25 So the company should set the price of a soda at 50 cents. 2 ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern