MATH 1090 Algebra and Trigonometry
Problem Set 5 - Questions

1. Sketch the graphs of the following quadratic functions.
   Indicate the locations of the vertex and all axis intercepts on your sketch.
   1. y   =   8 - 2(x + 3)²
   2. y   =   3x² - 6x + 5
   3. y   =   9 - x²

2. 300 metres of fencing is available to fence off a rectangular playing field that must also be divided into two areas by a fence parallel to a boundary fence.   Find the lengths of the fences that maximizes the total enclosed area and find that maximum area.

3. Sketch the graph of the function   f (x)   =   -2 (x - 4)² (x² - 25)

4. For the function   f (x)   =   x³ - 13 x² + 144 ,
   1. Find the roots of the equation   f (x) = 0 .
   2. Sketch the curve   y = f (x) .

5. Show that the function   x⁵ - x³ - 1   has a real zero between 1 and 2.
   Use the intermediate value theorem to find an approximation for that zero, correct to one decimal place.

6. Follow the seven steps on page 327 of the course textbook to graph each of the following rational functions.
   1. 
   2. 
   3. 

Also:   Try the questions from exercise sets 3.1 to 3.6 of the textbook.
The solutions to this problem set will appear elsewhere on this web site.

[Index of Questions]

[Problem Set & Quiz Solutions]