Rewrite the function in standard form
F(x) = 2(x - 3)^3 + 9
Show your work and explain it at a 9th grade level
To rewrite the function in standard form, we need to expand the equation and simplify it.
First, we expand the equation:
F(x) = 2(x - 3)^3 + 9
F(x) = 2(x - 3)(x - 3)(x - 3) + 9
F(x) = 2(x^2 - 6x + 9)(x - 3) + 9
F(x) = 2(x^3 - 6x^2 + 9x - 3x^2 + 18x - 27) + 9
F(x) = 2(x^3 - 9x^2 + 27x - 27) + 9
F(x) = 2x^3 - 18x^2 + 54x - 54 + 9
F(x) = 2x^3 - 18x^2 + 54x - 45
Therefore, the function in standard form is F(x) = 2x^3 - 18x^2 + 54x - 45.
In simpler terms, we expanded the given equation by multiplying out the terms. After simplifying and combining like terms, we were able to rewrite the function in standard form.