Answer: f(x) = x^2 - 4*x
Step-by-step explanation:
This is a quadratic equation, that can be written in factorized form as:
f(x) = A*(x - a)*(x - b)
Where A is a real number, a and b are the roots of the equation.
In the graph we can see that the graph intersects the x-axis at x = 0, and x = 4, then:
a = 0
b = 4
So the equation is:
f(x) = A*(x -0)*(x - 4) = A*x*(x - 4)
Now we can also see that, the arms of the exponential open up, this means that A is positive, and we also can see that f(2) = -4
Then:
f(2) = A*2*(2 - 4) = -4
= A*2*(-2) = -4
= A*-4 = -4
A = -4/-4 = 1
A = 1
Then the equation is:
f(x) = x*(x - 4) = x^2 - 4*x
