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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).`
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