Question 273823
# 1




{{{f(x)=3x^2-7x+1}}} Start with the given equation.



{{{f(-1)=3(-1)^2-7(-1)+1}}} Plug in {{{x=-1}}}.



{{{f(-1)=3(1)-7(-1)+1}}} Square {{{-1}}} to get {{{1}}}.



{{{f(-1)=3-7(-1)+1}}} Multiply {{{3}}} and {{{1}}} to get {{{3}}}.



{{{f(-1)=3+7+1}}} Multiply {{{-7}}} and {{{-1}}} to get {{{7}}}.



{{{f(-1)=11}}} Combine like terms.



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# 2


{{{f(x)=3x^2-7x+1}}} Start with the given equation.



{{{f(x+1)=3(x+1)^2-7(x+1)+1}}} Replace each 'x' with 'x+1'.



{{{f(x+1)=3(x^2+2x+1)-7(x+1)+1}}} FOIL



{{{f(x+1)=3x^2+6x+3-7x-7+1}}} Distribute



{{{f(x+1)=3x^2-x-3}}} Combine like terms.



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# 3


{{{f(x)=3x^2-7x+1}}} Start with the given equation.



{{{f(x+h)=3(x+h)^2-7(x+h)+1}}} Replace each 'x' with 'x+h'.



{{{f(x+h)=3(x^2+2xh+h^2)-7(x+h)+1}}} FOIL



{{{f(x+h)=3x^2+6xh+3h^2-7x-7h+1}}} Distribute