Write a polynomial function in standard form with zeros -1, -1, 6
y = a(x+1)^2 (x-6) , where a is any non-zero real number. More information such as a point on the function has to be given to find a.
To write a polynomial function in standard form with zeros -1, -1, and 6, we can start by factoring the function using the zero-factor property.
Since -1 is a zero twice, we know that the function will have a factor of (x + 1) multiplied by (x + 1) or (x + 1)^2.
The zero 6 will give us a factor of (x - 6).
Multiplying these factors together, we get:
f(x) = (x + 1)^2 * (x - 6)
Next, we can expand this equation:
f(x) = (x + 1)(x + 1)(x - 6)
To simplify this, we can use the distributive property:
f(x) = (x^2 + 2x + 1)(x - 6)
Expanding further:
f(x) = x^3 - 6x^2 + 2x^2 - 12x + x - 6
Combining like terms:
f(x) = x^3 - 4x^2 - 11x - 6
Therefore, the polynomial function in standard form with zeros -1, -1, and 6 is f(x) = x^3 - 4x^2 - 11x - 6.