Graph Of X 2

The Graph of x^2

The graph of x^2 is a parabola. It is a curve that opens up or down, depending on the value of a in the equation y = ax^2 + bx + c.

Properties of the Graph of x^2

The graph of x^2 has the following properties:

• It is symmetrical about the x-axis.
• The vertex of the parabola is the point (h, k) where the graph changes direction.
• The axis of symmetry is the vertical line that passes through the vertex.
• The focus of the parabola is a point on the axis of symmetry, a distance p units away from the vertex.
• The directrix of the parabola is a horizontal line that passes through the focus, a distance p units below the vertex if the parabola opens up, or a distance p units above the vertex if the parabola opens down.

How to Graph x^2

To graph x^2, you can use the following steps:

1. Find the vertex of the parabola.
2. Find the axis of symmetry.
3. Find the focus of the parabola.
4. Find the directrix of the parabola.
5. Plot the points that satisfy the equation y = ax^2 + bx + c.

Examples of Graphs of x^2

Here are some examples of graphs of x^2:

• y = x^2

The graph of y = x^2 is a parabola that opens up. The vertex of the parabola is (0, 0). The axis of symmetry is the x-axis. The focus of the parabola is (0, 1). The directrix of the parabola is the line y = -1.

[Image of Graph of y = x^2]

• y = -x^2

The graph of y = -x^2 is a parabola that opens down. The vertex of the parabola is (0, 0). The axis of symmetry is the x-axis. The focus of the parabola is (0, -1). The directrix of the parabola is the line y = 1.

[Image of Graph of y = -x^2]

• y = 2x^2

The graph of y = 2x^2 is a parabola that opens up. The vertex of the parabola is (0, 0). The axis of symmetry is the x-axis. The focus of the parabola is (0, 2). The directrix of the parabola is the line y = -2.

[Image of Graph of y = 2x^2]

Questions about the Graph of x^2

Here are some questions about the graph of x^2:

• What is the equation of the graph of a parabola that opens up and has a vertex at (2, 3)?
• What is the vertex of the graph of y = 3x^2 – 2x + 1?
• What is the focus of the graph of y = -x^2 + 2x – 1?
• What is the directrix of the graph of y = 2x^2 – 3x + 4?

Answers to Questions about the Graph of x^2

• The equation of the graph of a parabola that opens up and has a vertex at (2, 3) is y = 2(x – 2)^2 + 3.
• The vertex of the graph of y = 3x^2 – 2x + 1 is (1, 1).
• The focus of the graph of y = -x^2 + 2x – 1 is (0, 1).
• The directrix of the graph of y = 2x^2 – 3x + 4 is the line y = -2.

Conclusion

The graph of x^2 is a parabola. It is a curve that opens up or down, depending on the value of a in the equation y = ax^2 + bx + c.