Final answer:
To find a polynomial function with the given zeros and passes through a given point, we can use the fact that the zeros of a polynomial are the values of x where the graph of the polynomial crosses the x-axis.
Step-by-step explanation:
To find a polynomial function with the given zeros and passing through a given point, we can start by using the fact that the zeros of a polynomial are the values of x where the graph of the polynomial crosses the x-axis.
So, if we have zeros at -3, 2, and 5, we can write the equation as:
(x + 3)(x - 2)(x - 5) = 0
Now, we can expand this equation and multiply the binomials:
(x + 3)(x - 2)(x - 5) = 0
x³ - 4x² - 7x + 30 = 0
So, the polynomial function is f(x) = x³ - 4x² - 7x + 30. To check if the graph passes through the point (7, 200), we can substitute x = 7 into the equation:
f(7) = 7³ - 4(7)² - 7(7) + 30 = 200
Therefore, the graph of the polynomial function passes through the point (7, 200).