The y-intercept is (0, 0). The x-intercepts are (0, 0), (2, 0). Degree is 3. End behavior: as x → −∞, f(x) → −∞, as x → ∞, f(x) → ∞.

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Expert Solution

Consider a polynomial function of degree 3 and having following x-intercepts and y-intercepts respectively,

(0, 0) → y-intercept

(0, 0), (2, 0) → x-intercepts

End behavior of the polynomial function is,

x → ∞, f(x) → ∞

x → -∞, f(x) → -∞

The end behavior shows that the graph is upwards. This means take the leading coefficient 1.

Consider the following general form of a polynomial function of degree 3.

f(x) = a(x – 0)(x – 2)2

= x(x2 – 4x + 4)

f(x) = x3 – 4x2 + 4x

Hence, the polynomial function is f(x) = x3 – 4x2 + 4x.

Junaid answered 1 year ago

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