Question

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Answer 1

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