# How can I use a graph to write an algebraic function?

##### 1 Answer

From the graph you should be able to determine some

#### Explanation:

The number of point you need will depend upon the shape of the graph: 2 sets for a linear graph; 3 sets for a parabola and so on.

**Examples:**

**1. Linear Graph**

graph{(y-(5x-3))(x^2+(y+3)^2-0.01)((x-1)^2+(y-2)^2-0.01)=0 [-5.15, 7.337, -4.03, 2.213]}

2 possible points that could be read from this graph:

General form of a linear equation (one version):

Using the points we read from the graph for

Two equations in two variables can be easily solved as :

So the equation can be written as

**2. Parabolic Graph**

graph{(y-(3*x^2 -2x +4))((x-1)^2+(y-5)^2-0.01)((x+1)^2+(y-9)^2-0.01)(x^2+(y-4)^2-0.01)=0 [-4.23, 6.87, 3.568, 9.115]}

3 possible points that could be read from this graph:

Using the general form for a parabola of:

and the points we read from the graph:

Again (without the details) we have 3 equations in 3 variables that can be solved as

So the equation can be written as

More complex polynomials will require more points but the process is identical.