Question

Write g(x) = 4x2 + 88x in vertex form. The function written in vertex form is g(x) = ___ (x +11)2 +____.

Answer 1

To keep it simple the answer is g(x) = 4 (x+11) ^2 + -484

The 4 stays the same and then the -484 is 88 multiply by -5.5.

Answer 2

`The\ vertex\ form:\\\\f(x)=a(x-h)^2+k`

`\text{Use}\ (a+b)^2=a^2+2ab+b^2\qquad(*)`

`g(x)=4x^2+88x=4(x^2+22x)=4(x^2+2\cdot x\cdot11)\\\\=4(\underbrace{x^2+2\cdot x\cdot11+11^2}_((*))-11^2)=4[(x+11)^2-121]=4(x+11)^2+(4)(-121)=4(x+11)^2-484`