Click on this link for a file that has Mapping Diagram blanks (2 and 3 axes) for use in the following exercises.
1. For each quadratic function complete the function table and then create the corresponding mapping diagram and locate the "extreme point".

a.
 $x$ $f(x)=2x^2$ 2 1 0 -1 -2

b.
 $x$ $f(x)= -2x^2$ 2 1 0 -1 -2

c.
 $x$ $f(x)= -x^2 + 1$ 2 1 0 -1 -2
d.
 $x$ $f(x)= x^2+1$ 2 1 0 -1 -2
2. For each quadratic function complete the function table and then create the corresponding mapping diagram and locate the "extreme point".

a.
 $x$ $f(x)=\frac 1 2 x^2$ 2 1 0 -1 -2

b.
 $x$ $f(x)=-\frac 1 2 x^2$ 2 1 0 -1 -2

c.
 $x$ $f(x)=\frac 1 2 x^2 + \frac 1 2$ 2 1 0 -1 -2
d.
 $x$ $f(x)=-\frac 1 2 x^2 + \frac 1 2$ 2 1 0 -1 -2
3. For the quadratic functions in problem 1 and 1 d,  find any values of $a$ where $f(a) = 0$.
4. For the quadratic functions in problem 2 and 2 d,  find any values of $a$ where $f(a) = 0$.
5. Suppose $f$ is a quadratic function with its extreme value at $x=1$ with $f(1)= 3$ and $f(3) = 1$.
a. Determine $A$, the magnification factor of $f$.
b. Use the value of A to find $f(0)$ and $f(2)$. Discuss how the magnification constant effects this mapping diagram
c. Give the vertex magnification  and the standard forms for $f$ based on the given information.
d. Solve the equation $f(x) = 0$ and display the approximate solutions on your mapping diagram.
e. Discuss the symmetry of your diagram.
6. For each  quadratic function  create a mapping diagram for the function treated as a composition of core linear functions and the core quadratic function $q(x)=x^2$.
a. $f(x)=2x^2 + 1$                   b. $f(x)= -2(x-1)^2 - 3$
c. $f(x)=\frac 1 2 x^2 + \frac 1 2$            d.  $f(x)=-\frac 1 2 (x+1)^2 + \frac 1 2$
7.  For each quadratic function  use "socks and shoes" to find and create a mapping diagram for the function for its inverse function for the domain $[0,\infty)$.
a. $f(x)=2x^2 + 1$                        b. $f(x)= -2x^2 - 3$
c. $f(x)=\frac 1 2 x^2 + \frac 1 2$            d.  $f(x)=-\frac 1 2 x^2 + \frac 1 2$