Graphs of X^2
In mathematics, a graph of a function is a visual representation of the function. It is created by plotting the points of the function in the coordinate plane.
The graph of x^2 is a parabola. It is defined as the set of all points (x, x^2) in the coordinate plane.
To graph x^2, we can start by plotting the points (0, 0), (1, 1), (2, 4), and so on. As we continue to plot points, we will see that the graph forms a parabola.
The parabola of x^2 opens upward. It has a vertex at the origin (0, 0). The axis of symmetry of the parabola is the x-axis.
The graph of x^2 can be used to represent a variety of real-world situations. For example, it can be used to represent the height of a projectile as it travels through the air, or the distance a ball rolls down a hill.
Questions about the graph of x^2:
- What is the vertex of the graph of x^2?
- What is the axis of symmetry of the graph of x^2?
- What is the range of the graph of x^2?
- What is the domain of the graph of x^2?
Answers:
- The vertex of the graph of x^2 is the point (0, 0).
- The axis of symmetry of the graph of x^2 is the x-axis.
- The range of the graph of x^2 is all real numbers greater than or equal to 0.
- The domain of the graph of x^2 is all real numbers.
Additional questions:
- What is the slope of the line tangent to the graph of x^2 at the point (1, 1)?
- What is the equation of the line tangent to the graph of x^2 at the point (0, 0)?
- What is the area enclosed by the graph of x^2 and the x-axis between the points (-1, 1) and (1, 1)?
Answers:
- The slope of the line tangent to the graph of x^2 at the point (1, 1) is 2.
- The equation of the line tangent to the graph of x^2 at the point (0, 0) is y = x.
- The area enclosed by the graph of x^2 and the x-axis between the points (-1, 1) and (1, 1) is 1/2.
These are just a few questions that can be asked about the graph of x^2. There are many other questions that can be asked, depending on the specific context in which the graph is being used.
