Analytic Geometry Self Quiz Solutions
1) For the parabola given by 
, find its vertex.
= -1 and f(-1) = 2(-1)2 + 4(-1) – 3 = 2 – 4 – 3, or -5.
So, our vertex is the point 
.
If you struggled with this problem, look at the module Finding the Vertex of a Parabola.
2) Determine the inverse of the function 
.
So, the inverse of the function 
is 
If you struggled with this problem, look at the module Inverses of Functions.
3) Determine the symmetry of the graphs of these functions.
a) 
First, we’ll check for y-axis symmetry:
So, this function does not have y-axis symmetry. Now we check for origin symmetry.
So, this function does not have origin symmetry either.
b) 
Let’s first test for y-axis symmetry:
This function is symmetric with respect to the y-axis.
Since g(-a) = g(a), we will not have g(-a) = -g(a) since g(a) =g(-a). This function is not symmetric about the origin.
If you struggled with this problem, look at the module Types of Symmetry.
4) Determine the points of intersection of 
and 
.
So, the two graphs intersect at the points 
and 
.
If you struggled with this problem, look at the module Finding Points of Intersection.
5) Determine the minimum degree, whether the degree is odd or even, and whether the leading coefficient is positive or negative for the polynomials given by the following graphs.
a) The degree of this polynomial is odd, the degree must be at least three, and the leading coefficient is negative.
b) The degree of this polynomial is even, the degree must be at least four, and the leading coefficient is negative.
c) The degree of this polynomial is odd, the degree must be at least five, and the leading coefficient is positive.
If you struggled with this problem, look at the module Classifying Polynomials by Their Graphs.
6) Determine the center and radius of the circle given by the equation 
:
So, the center is the point 
and the radius is 2.
If you struggled with this problem, look at the module Graphs and Equations of Circles.
7) Determine the x and y intercepts of the graph 
.
First, the y-intercept:
So, the y-intercept is 3.
Now, the x-intercept(s):
So, the x-intercepts are -1 and -3.
If you struggled with this problem, look at the module Finding x, y Intercepts.