How to solve the quadratic equation graphically

Quadratic equations can be solved both using formulas and graphically. The last method is a little more complicated, but the solution will be visual, and you will understand why the quadratic equation has two roots and some other laws.

Where to start the graphical solution

Let there be a complete quadratic equation: A * x2 + B * x + C = 0, where A, B and C are any numbers, and A is not equal to zero. This is a general case of a quadratic equation. There is also a reduced form in which A = 1. To solve any equation graphically, you need to transfer the term with the greatest degree to another part and equate both parts to a variable.

After that, A * x2 will remain on the left side of the equation, and B * xC on the right side (we can assume that B is a negative number, this does not change the essence). We get the equation A * x2 = B * xC = y. For clarity, in this case, both parts are equated to the variable y.

Charting and processing of results

Now we can write two equations: y = A * x2 and y = B * xC. Next, you need to build a graph of each of these functions. The graph y = A * x2 is a parabola with a vertex at the origin, the branches of which are directed up or down, depending on the sign of A. If it is negative, the branches are directed down, if positive, up.

The graph y = B * xC is a normal straight line. If C = 0, the line passes through the origin. In the general case, it cuts off a segment equal to C from the ordinate axis. The slope of this line relative to the abscissa is determined by the coefficient B. It is equal to the slope of this angle.

After the graphs are built, it will be seen that they intersect at two points. The coordinates of these points along the abscissa axis determine the roots of the quadratic equation. For their exact definition, you need to clearly build graphs and choose the right scale.