Which polynomial function has x intercepts -1, 0, and 2 and passes through the point (1, -6)?
f(x) = x³ - x²  - 2x
f(x) = 3x³ - 3x² - 6x
f(x) = x³ + x² - 2x
f(x) = 3x³ + 3x² - 6x

Solution:

We know that the equation of a polynomial function with x-intercepts as -1, 0, 2 is

f(x) = a(x - (x - 1))(x - 0)(x - 2)

= a[x(x + 1)(x - 2)]

= a(x³ - x² - 2x)

It passes through the point (1, -6)

⇒ a(1³ - 1² - 2(1)) = -6

⇒ a (1 - 1 - 2) = -6

⇒ -2a = -6

Divide both sides by -2

⇒ a = 3

So we get,

f(x) = 3(x³ - x² - 2x) = 3x³ - 3x² - 6x

Therefore, the polynomial function which has x intercepts -1, 0, and 2 and passes through the point (1, -6) is f(x) = 3x3 - 3x2 - 6x.

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Which polynomial function has x intercepts -1, 0, and 2 and passes through the point (1, -6)?

Summary:

The polynomial function which has x intercepts -1, 0, and 2 and passes through the point (1, -6) is f(x) = 3x³ - 3x² - 6x.