If f(x) = -2x^2 + 2x -2f(x)=−2x2+2x−2. what is f(a-1)f(a−1)?

1 Answer
mason m
Dec 31, 2015

f(a-1)=-2a^2+6a-6f(a−1)=−2a2+6a−6

Explanation:

Replace each xx with (a-1)(a−1), then simplify.

f(a-1)=-2(a-1)^2+2(a-1)-2f(a−1)=−2(a−1)2+2(a−1)−2

First, distribute the squared terms. You can either write out (a-1)(a-1)(a−1)(a−1) and distribute to find that it's equal to a^2-2a+1a2−2a+1 or use the rule that (a-b)^2=a^2-2ab-b^2(a−b)2=a2−2ab−b2.

=>-2(a^2-2a+1)+2(a-1)-2⇒−2(a2−2a+1)+2(a−1)−2

Distribute the -2−2 and 22. Remember that multiplying a negative by a negative will result in a positive.

=>-2a^2+4a-2+2a-2-2⇒−2a2+4a−2+2a−2−2

Group like terms.

=>-2a^2+(4a+2a)+(-2-2-2)⇒−2a2+(4a+2a)+(−2−2−2)

Add.

=>-2a^2+6a-6⇒−2a2+6a−6

Optionally factored:

=>-2(a^2-3a+3)⇒−2(a2−3a+3)

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