Final answer:
To find the x and y intercepts of the polynomial function f(x)=-2(x+3)(x-5)^2, plug in x=0 to find the y-intercept and set y=0 to find the x-intercepts (-3,0) and (5,0).
Step-by-step explanation:
To find the x and y intercepts of the polynomial function f(x)=-2(x+3)(x-5)^2, we first set x=0 to find the y-intercept. Plugging in x=0 into the function, we get f(0)=-2(0+3)(0-5)^2 = -2(3)(25) = -150. So, the y-intercept is (0, -150).
To find the x-intercepts, we set y=0 and solve for x. Setting y=0 in the function, we get 0=-2(x+3)(x-5)^2. Since a product is equal to zero if and only if one of its factors is zero, we set each factor equal to zero and solve for x. We have x+3=0 or x-5=0. Solving these equations, we find x=-3 or x=5. So, the x-intercepts are (-3, 0) and (5, 0).