Create an equation whose graph has intercepts at (-5,0), (0,0) and (5,0)

We notice that the graph is passing through the points (-5
; 0) , (5 ; 0) and origin (0 ; 0) of the system of coordinates. Since the graph is
intercepting x axis 3 times, that means that the equation has three roots: x = -5 ; x =
0 and x = 5

Since we know the roots, we can write the
equation of the function  as a product of linear factors.

y
= (x - x1)(x - x2)(x - x3), where x1, x2 and x3 are the roots of the
equation.

The roots of the equation that have to be created
are x1 = -5 ; x2 = 0 and x3 = 5, therefore the equation
is:

`y = (x - 0)(x - 5)(x +
5)`

The special product (x-5)(x+5) returns the difference
of two squares:

`y = x(x^2 -
25)`

Therefore, the equation whose graph ha
sthe intercepts (-5 ; 0) ; (0 ; 0) ; (5 ; 0) is:` y = x(x^2 - 25).`