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.
Rewrite the function in standard form
F(x) = 2(x - 3)^3 + 9
Show your work and explain it at a 9th grade level
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