Question

Which function in vertex form is equivalent to f(x) = x² + x +1?

Answer 1

Answer:

$\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}$

Step-by-step explanation:

NOTE :

$x^2+ax=\left( x+\frac{a}{2} \right)^{2} -\left( \frac{a}{2} \right)^{2}$

………………………………………

f(x) = x² + x +1

     $=x^{2}+2\times \frac{x}{2} +1$

     $=\left( x+\frac{1}{2} \right)^{2} -\left( \frac{1}{2} \right)^{2} +1$

     $=\left( x+\frac{1}{2} \right)^{2} - \frac{1}{4}+1$

     $=\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}$