Answer:
f(x) = 0.5x^3 + 2.5x^2 - 75x
Explanation:
To write the equation of a polynomial with given x-intercepts and passing through a point, we can use the factored form of the polynomial:
f(x) = a(x - r1)(x - r2)(x - r3) ...
where r1, r2, r3, ... are the x-intercepts, and a is a constant that scales the polynomial vertically. Since the x-intercepts are 0, 10, and -15, we can write:
f(x) = a(x - 0)(x - 10)(x + 15)
Expanding this expression gives:
f(x) = a(x^3 + 5x^2 - 150x)
To find the value of a, we can use the fact that the polynomial passes through the point (2, -136):
-136 = a(2^3 + 5(2^2) - 150(2))
Simplifying this equation gives:
-136 = -272a
Dividing both sides by -880 gives:
a = 0.5
Therefore, the equation of the polynomial is:
f(x) = 0.5x^3 + 2.5x^2 - 75x