Subjects
Grades
The Square Root Function
Concept sheet | Mathematics
Secondary
4-5
The equation of the square root function is written |f(x)=a\sqrt{bx}|, where |a| and |b| are both non-zero.
Note: When |a=1| and |b=1|, we get the equation |f(x)=\sqrt{x}| which corresponds to the basic form of the square root function.
This concept sheet explores the square root function and the behavior of its parameters. For more details, see the following concept sheets.
- The Graph and Properties of the Square Root Function |f(x)=a\sqrt{bx}|
- The Role of the Parameters of a Square Root Function
- Sketching the Graph of a Square Root Function
- Finding the Equation of a Square Root Function
- The Properties of the Square Root Function
- Solving an Equation or Inequality with a Square Root
- Solving Problems Involving the Square Root Function
- The Inverse of the Square Root Function
The Graph and Properties of the Square Root Function|f(x)=a\sqrt{bx}|
If we denote the area of a square by |x| and the length of a side by |y|, we obtain the equation |f(x)=\sqrt{x}|. Here, |a=1| and |b=1|. The graph below illustrates the square root function.
| |x| | |y| |
|---|---|
| |1| | |1| |
| |4| | |2| |
| |9| | |3| |
| |16| | |4| |
Notice that the function has a vertex, which is always located at the origin |(0,0)| when the equation is of the form |f(x)=a\sqrt{bx}.|