From the graphs attached, graph shown in the bottom left will be the correct option.
Given polynomial function in the question is,
To find the correct graph for this polynomial we will find the roots first.
For which factorize the given polynomial.
f(x) = x³ + 4x²- 4x - 16
= x²(x + 4) - 4(x + 4)
= (x² - 4)(x + 4)
= (x - 2)(x + 2)(x + 4) [Since, (x² - 4) = (x - 2)(x + 2)]
For f(x) = 0,
(x - 2)(x + 2)(x + 4) = 0
⇒ x = -2, -4, 2
These roots reveal that curve of the polynomial function intersects the x-axis at (-2, 0), (-4, 0) and (2, 0).
From the given option, graph in the bottom left will be the answer.
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