What is the standard form of #f(x)=(x-1)^2-(3x+4)^2 #?

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Answer 1 · 2016-03-08T04:16:33

Standard form is #f(x)=-8x^2-26x-15#

Standard form of quadratic polynomial with one variable is #f(x)=ax^2+bx+c#.

Hence to convert #f(x)=(x−1)^2−(3x+4)^2#, one should expand the RHS, using identity #(a+-b)^2-a^2+-2ab+b^2#

#f(x)=(x−1)^2−(3x+4)^2#

= #x^2-2x+1-((3x)^2+2xx3x xx4+4^2)# or

= #x^2-2x+1-(9x^2+24x+16)#

= #x^2-2x+1-9x^2-24x-16#

= #-8x^2-26x-15#