Note that the graph is indeed a function as it passes the vertical line test. and is shared by the graphs of all quadratic functions. Therefore, the quadratic equation x 2 + 4x + 8 = 0 does not have any real roots.This general curved shape is called a parabola The U-shaped graph of any quadratic function defined by f ( x ) = a x 2 + b x + c, where a, b, and c are real numbers and a ≠ 0. In this example, the curve does not touch or cross the x -axis. Solve the equation x 2 + 4x + 8 = 0 by graphical method. Therefore, 6 x – 9 – x 2 = 0 has one solution(x = 3). Therefore, the roots of the quadratic equation are x = 1.3 and x = –2.3 Our arbitrary values are shown in the table below: Solve the equation x 2 + x – 3 = 0 by graphical method In these examples, we have drawn our graphs using graphing software, but for you to understand this lesson very well, draw your graphs manually. Let’s graph a few examples of quadratic equations.
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