Instruction

1

Any chart you can specify a particular function. To find the points at which the graphs intersect, we need to solve the equation which has the form: f₁(x)=f₂(x). The result of the decision would be the point (or points) that you are looking for. Consider the following example. Let the value y₁=k₁x+b₁, and the value y₂=k₂x+b₂. To find the points of intersection on the x-axis it is necessary to solve the equation y₁=y₂, that is k₁x+b₁=k₂x+b₂.

2

Convert the given inequality, getting k₁x-k₂x=b₂-b₁. Now Express x: x=(b₂-b₁)/(k₁-k₂). Thus you will find the point of intersection of the graphs, which is on the axis OX. Find the point of intersection on the y-axis. Just set any of the functions of the x value that you found earlier.

3

The previous option is suitable for linear function graphs. If the function is quadratic, use the following instructions. In the same way as with a linear function, find the value of x. To do this, solve the quadratic equation. In the equation 2x2 + 2x - 4=0 find the discriminant (equation given as an example). To do this, use the formula: D= b2 – 4ac, where b is a value before X, and c is a numeric value.

4

Substituting numerical values, we obtain an expression of D= 4 + 4*4= 4+16= 20. The value of the discriminant affects the roots of the equation. Now to the value of the variable b with the sign "-" add or subtract (in turn) the root of the resulting discriminant, and divide by twice the product of the coefficient a. So you will find the roots of the equation, i.e. the coordinates of the points of intersection.

5

Graphs of quadratic functions have a feature: the x-axis will intersect twice, then there you will find two coordinates of the x-axis. If you receive periodic dependency of X from Y, then know that the graph intersects in an infinite number of points with the abscissa axis. Check whether you found the point of intersection. To do this, substitute the value of X in the equation f(x)=0.