Note some of the differences between the given linear and quadratic functions by recognizing that

  • this particular quadratic function squares the input values (x-values), making all output values (f(x) -values) positive.
  • the f(x) -values of this quadratic function are restricted to those greater than or equal to zero and therefore the range is .
  • with the exception of the lowest point on the graph of the parabola, all other points on the parabola have a mirror image point because of the symmetry about the vertical axis. This means that points with x-coordinates of x and −x will have the same f(x) -coordinate because they are equidistant from the line of symmetry (in this case, the vertical axis). For example, for x = 2 and x = −2, the f(x) -coordinate is the same, 4.


Not all quadratic functions are as basic as simply squaring the input value and not all graphs of quadratic functions are symmetrical about the vertical axis, as you will see in the following Practice Run.