Dr. Byrne
Fall 2010
Math 112
Take Home Quiz #15: Review Lines and Parabolas
1. Equations for lines.
a. Make up two points (x,y) such that all the x-coordinates and y-coordinates are
different. Find the equation of the line that goes through those 2 points in the
form y=mx+b. Then check that your equation is correct by making sure that
both points are on your line. (That is, plug in the x value and make sure you
would get out the y value.) For full credit, you must complete all the steps in
this problem.
b. Make up two points (x,y) such that the x-coordinates of the two points are the
same. Find the equation of the line that goes through those 2 points in the
form y=mx+b. Then check that your equation is correct by making sure that
both points are on your line. (That is, plug in the x value and make sure you
would get out the y value.) For full credit, you must complete all the steps in
this problem.
c. Make up two points (x,y) such that the y-coordinates of the two points are the
same. Find the equation of the line that goes through those 2 points in the
form y=mx+b. Then check that your equation is correct by making sure that
both points are on your line. (That is, plug in the x value and make sure you
would get out the y value.) For full credit, you must complete all the steps in
this problem.
2. Piecewise defined functions naturally occur in many contexts. For example, suppose
that the amount of money that a class earns for selling boxes of cookies is as follows:
# of boxes sold
0-10
11-50
>50
money earned for class
none
$50
$100
Then the amount of money earned could be described with a piecewise function,
where x is the number of boxes sold:
 0, if 0  x  10

f ( x)  50, if 11  x  50 .
 50, if x  50

Find your own real-life context where a piecewise function could be applied.
Describe the context and write down the piecewise function.
3. Obtaining information from quadratic equations in different forms.
a. In standard form, f ( x)  3x  7   2 . What is the vertex of this parabola?
What is the y-intercept?
2
b. In factored form g ( x)  1x  7x  3 . What are the zeros of this function?
What is the y-intercept?