Writing an Equation of a Cubic Polynomial Function
What is the equation of the cubic polynomial function with zeroes at (2, 0), (3, G), and (5, 0) passing through the coordinate (0, -5)?
Recall that the zeroes are (2, 0), (3, G), and (5, 0).
What is the y-intercept of this graph?
Options:
O-5
O
-2
3
5
Equation of the cubic polynomial function:
The equation of the cubic polynomial can be determined using the given zeros: (2, 0), (3, G), and (5, 0). By multiplying the factors, we get:
f(x) = x^3 - 10x^2 + 31x - 30
Y-intercept of the graph:
The y-intercept of the graph is -30.
To find the equation of the cubic polynomial function with zeroes at (2, 0), (3, G), and (5, 0) passing through the coordinate (0, -5), we use the given zeros to express the factors as (x - 2), (x - 3), and (x - 5). Multiplying these factors together gives us:
f(x) = (x - 2)(x - 3)(x - 5)
Expanding and simplifying the expression, we get:
f(x) = x^3 - 10x^2 + 31x - 30
Therefore, the equation of the cubic polynomial function is f(x) = x^3 - 10x^2 + 31x - 30.
To determine the y-intercept, we substitute x = 0 into the equation and solve for y:
f(0) = 0^3 - 10(0)^2 + 31(0) - 30
f(0) = -30
Thus, the y-intercept of the graph is -30.