Question

Which polynomial function has x-intercept s -1,0, and 2 and passes through the point (1,-6)? f(x)=x^(3)-x^(2)-2x f(x)=3x^(3)-3x^(2)-6x f(x)=x^(3)+x^(2)-2x f(x)=3x^(3)+3x^(2)-6x

Answer 1

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

Step-by-step explanation:

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

To find this, we can substitute the values of the x-intercepts into the function to confirm if they are zeros of the polynomial. Then, we can substitute the point (1,-6) into the function to check if it satisfies the equation.

For example, for f(2) = 2³ - 2² - 2(2) = 8 - 4 - 4 = 0, and for f(1) = 1³ - 1² - 2(1) = 1 - 1 - 2 = -2, which confirms that the function satisfies the given conditions.