Linear and Quadratic Functions: Graphing Quadratic Functions

The Value of "k"

The letter "k"

The value of "k" in the function f(x) = a(x – h)2 + k describes how the parent function moves up or down.

Analyze the following graph:

Graph 1 is f of x equals x squared. Graph 2 is f of x equals x squared plus two. Graph 3 is f of x equals x squared minus two.

  1. The red graph is the parent function f(x) = x2.
  2. The blue graph represents f(x) = x2 + 2.
  3. The green graph represents f(x) = x2 – 2.

If we analyze the "k" value for all three functions we notice that a "k" value greater than zero moves the function up the absolute value of k units. A "k" value less than zero moves the function down the absolute value of k units.

k > 0 moves the parent function f(x) = x2 up the absolute value of k units.

k < 0 moves the parent function f(x) = x2 down the absolute value of k units.