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

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

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

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

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