Graphing pure quadratic equations

Graph of pure quadratic equation y = x^2 - 4

In graphing a quadratic equation, you should first get its vertex coordinates, and then the two x-intercepts. These three points enable you to draw the parabola of the pure quadratic equation.



Vertex coordinates

x-coordinates

The most important point to remember is that the vertex of a pure quadratic equation lies on the y-axis. That is, the x-coordinate of the vertex of a pure quadratic equation is zero. Thus, the vertex coordinates of a pure quadratic equation can be represented by (0, y).

y-coordinates

In order to obtain the y-coordinate of the vertex of a pure quadratic equation, plug in x = 0 in the equation and you will get the y-intercept. For example, for the pure quadratic equation y = x² - 4, the y-intercept is y = (0)^2 - 4 = 4. Hence its vertex coordinates are (0, -4)

x-intercepts

The x-intercepts of a parabola are present at y = 0. Thus, plugging in y = 0 in the pure quadratic equation, you will get the x-intercepts. For example, for the pure quadratic equation y = x² - 4, plugging in y = 0, you obtain:

0 = x² - 4

x² = + 4

x = √+4

x = +2 or x = -2

Thus, the two x-intercepts of the pure quadratic equation y = x² - 4 are at x = 2 and x = -2, or at the points (2, 0) and (-2, 0).

Plotting the vertex and x-intercepts of y = x² - 4 obtained above, you will obtain the above graph. (Click on the above graph to see full size image)