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

1 Answer
mason m
Dec 31, 2015

#f(a-1)=-2a^2+6a-6#

Explanation:

Replace each #x# with #(a-1)#, then simplify.

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

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

#=>-2(a^2-2a+1)+2(a-1)-2#

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

#=>-2a^2+4a-2+2a-2-2#

Group like terms.

#=>-2a^2+(4a+2a)+(-2-2-2)#

Add.

#=>-2a^2+6a-6#

Optionally factored:

#=>-2(a^2-3a+3)#

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