MATH 1090 Algebra and Trigonometry
Problem Set 5 - Questions
2002 Winter
Note:
Without the Symbol font, the symbol
(not equals) appears as ¹ ,
the symbol
(right arrow) appears as ®
and the symbol
(square root) appears as Ö.
Sketch the graphs of the following quadratic functions.
Indicate the locations of the vertex and all axis intercepts on your
sketch.
y = 8 -
2(x + 3)2
y = 3x2
- 6x + 5
y = 9 -
x2
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.
Sketch the graph of the function f (x)
=
-2 (x -
4)2 (x2 - 25)
For the function f (x) =
x3 -
13 x2 + 144 ,
Find the roots of the equation f (x) = 0 .
Sketch the curve y = f (x) .
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.
Follow the seven steps on page 327 of the course textbook to graph
each of the following rational functions.
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.