Final answer:
To write the equation of a cubic polynomial function with the same zeroes and passing through a coordinate, determine the factors of the polynomial using the zeroes. The equation is formed by multiplying the factors. Substitute the given coordinate to find the value of the constant. The y-intercept of the graph is -5.
Step-by-step explanation:
To write the equation of a cubic polynomial function, we first determine the factors of the polynomial using the given zeroes. The zeroes are (2, 0), (3, 0), and (5, 0). Since the polynomial has the same zeroes and passes through the coordinate (0, -5), the y-intercept is -5.
The equation of the cubic polynomial function is formed by multiplying the factors of the zeroes. In this case, the factors are (x - 2), (x - 3), and (x - 5). So, the equation becomes:
f(x) = k(x-2)(x-3)(x-5)
where k is a constant. Since the polynomial passes through the point (0, -5), substituting the values in the equation:
-5 = k(0-2)(0-3)(0-5)
-5 = k(-2)(-3)(-5)
-5 = -30k
k = 5/30
Therefore, the equation of the cubic polynomial function is:
f(x) = (5/30)(x-2)(x-3)(x-5)
The y-intercept of this graph is -5, option 1.