Graph of a Square Function
Graph of a square function is Concave up or Concave down. It means the graph of the square function will be either open upwards or inverted(downwards).
For Example, take f(x) = ax2
Graph of the square function depends on the coefficient of x2,
- If the coefficient (a) is positive (a > 0) then the graph is concave up, f(x) has the minimum value.
- If the coefficient (a) is negative (a<0) then the graph is concave down, f(x) has the maximum value.
For example: Let us consider a square function y = x2
Substitute different x values in y,
- Substitute x = 3
y = 32 = 9
- Substitute x = -3
y = (-3)2 = 9
- Substitute x = 1
y = 12= 1
- Substitute x = -1
y = (-1)2= 1
- Substitute x = 0
y = 02 = 0
Take these calculated values in table as shown below,
x | y |
|---|---|
|
-3 |
9 |
|
-1 |
1 |
|
0 |
0 |
|
1 |
1 |
|
3 |
9 |
Plot these points and join them on the graph as shown below, having x-axis and y-axis,
Graph
Compare y = ax2 with y = x2,
as a = 1 which is a > 0, So the graph is concave up and f(x) has minimum value of (x, y) = (0, 0).
This minimum point is called vertex. The line that passes through this vertex is called the Axis of symmetry.
Axis of Symmetry: It is the line that divides the graph into two equal parts.
For y = x2, axis of symmetry is,
Take x-coordinate of vertex,
x = 0 is the axis of symmetry
Square Function
A square function is also a quadratic function. A square function is represented as f(x) = x2. The graph of the square function is in the shape of a parabola or U- shaped. Based on the coefficient of x2 (highest degree in a square function), the graph may be U- shaped or Inverted U- shaped.
In this article we have covered, the definition of a square function, the graph of a square function, the domain and range of a square function and others in detail.
Table of Content
- What is a Square Function?
- Graph of a Square Function
- Domain of a Square Function
- Range of a Square Function
- Properties of Square Function
- Conclusion
- Examples on Square Function
- Practice Questions on Square Function