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Answer:
Part A
Please find attached the graph of the function g(x) = (x + 2)·(x - 1)·(x - 2) created with MS Excel
Part B
Please find attached the parabola created with MS Excel
The shape of the parabola = cup shape
y-intercept is y = 4
The zeros, is x = 2
Part C
Please find attached the graph of the combined coaster created with MS Excel
Step-by-step explanation:
Part A
The maximum number of x-intercepts of a third degree polynomial is between 1 and 3, however, the third degree polynomial can have a y-intercept to make the number of intercepts = 3 + 1 = 4 intercept
a) For the function, g(x) = (x + 2)·(x - 1)·(x - 2), we have;
b) The x-intercepts which are the zeros of the function are;
x = -2, x = 1, and x = 2
The end behavior are;
When x → -∞, y → -∞, x → ∞, y → ∞
The y-intercept is y = (0 + 2)·(0 - 1)·(0 - 2) = 4
The y-intercept is y = 4
(ii) Please find attached the graph of the function created with MS Excel
Part B
The form of the parabola is f(x) = (x - a)·(x - b)
For a y-intercept of 4, we have;
f(x) = (x - 2)·(x - 2) = x² - 4·x + 4
Given that the coefficient of x² is negative, we have;
The parabola is opened up (cup shaped)
The y-intercept = 4
The zero is x = 2
Part C
Please find attached the combined coaster created with MS Excel
