Graph X 2 X 2

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.