# How to graph x squared?

The graph of the function y = x^2 is a curve that is called a parabola. To sketch this parabola, we should determine the vertex, y-intercept, x-intercept, and a few other points on both sides of the vertex of the curve. Afterward, a parabola is sketched through these points.

## Expert Answers

The function y = x^{2} is called a quadratic function because the highest degree of its terms is 2.

The standardized form of a quadratic function is y = ax^{2}+bx+c , where a, b, and c are real numbers and a \ne 0 . Note that if a = 0,...

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The function y = x^{2} is called a quadratic function because the highest degree of its terms is 2.

The standardized form of a quadratic function is y = ax^{2}+bx+c , where a, b, and c are real numbers and a \ne 0 . Note that if a = 0, then we obtain a linear equation. When graphed on the cartesian plane, the graph of this function yields a curve that is called a parabola. A parabola is a u-shaped curve that can open upwards or downwards.

To graph the function y = x^{2} on the cartesian plane, we need to obtain the following points:

- Vertex of the parabola: this is the turning point of the curve. It can be a minimum point or a maximum point. If it is a minimum point, then the curve opens upwards. However, if it is a maximum point, the curve opens downwards. The formula for calculating the x-coordinate of the vertex is x = \frac{-b}{2a} , where a and b are the coefficients of x^{2} and x , respectively.

For y = x^{2} , a = 1, b=0, and c = 0. Thus, x = \frac{-0}{2} = 0 .

When x = 0, y = 0^{2} = 0 ; thus, the coordinates of the vertex are (0, 0).

-y-intercept: this is the point where the curve cuts the y-axis. At this point, x = 0. Therefore, in the function y=x^{2} , when x = 0, y = 0^{2} = 0 ; thus, the coordinates of the y-intercept are (0, 0).

-x-intercept: this is the point where the curve cuts the x-axis. At this point, y=0. Therefore, when y = 0, then x^{2} = 0 , and x = 0. Thus, the coordinates of the x-intercept are (0, 0).

- Finally, we can determine the coordinates of a few more points on both sides of the vertex of y = x^{2} . We do this as follows:

When x = -2, y = (-2)^{2} = 4 ; the coordinates of this point are(-2, 4).

When x = -1, y = (-1)^{2} = 1 ; the coordinates of this point are (-1, 1).

When x = 0, y = 0; (0, 0).

When x = 1, y = (1)^{2} = 1 ; the coordinates of this point are (1, 1).

When x = 2, y = (2)^{2} = 4 ; the coordinates of this point are (2, 4).

Having found the points that the parabola passes through, we can now plot them and sketch a parabola through them. Please refer to the attached graph.

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