Click on this link for a file that has Mapping Diagram blanks (2 and 3 axes) for use in the following exercises.
You may want to try this using a spreadsheet. You can download a spreadsheet template for linear functions by clicking here.
Download worksheet for this section: Worksheet.QF.pdf.
  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 c  and 1 d,  find any values of $a$ where $f(a) = 0$.
  4. For the quadratic functions in problem 2 c  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.  $f(x)=-\frac 1 2 x^2 + \frac 1 2$