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

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

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

The x-intercepts of a parabola are present aty = 0. Thus, plugging iny = 0in the pure quadratic equation, you will get the x-intercepts. For example, for the pure quadratic equationy = x, plugging in^{2}- 4y = 0, you obtain:

0 = x^{2}- 4

x^{2}= + 4

x = √+4

x = +2orx = -2

Thus, the two x-intercepts of the pure quadratic equationPlotting the vertex and x-intercepts ofy = xare at^{2}- 4x = 2andx = -2, or at the pointsand(2, 0).(-2, 0)

*y = x*obtained above, you will obtain the above graph. (Click on the above graph to see full size image)

^{2}- 4
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