How to transform $ax^2+bx+c$ into $p(x-h)^2 +k$?

Question

How to transform $ax^2+bx+c$ into $p(x-h)^2 +k$?

For example, if I have this form: $$8x^2+3x+5$$, how can render it in the $p(x-h)^2 +k$ format?

Answer 1

As user Deepak mentioned: $$ h=-\frac{b}{2a}=-\frac{3}{16},\quad{k}=\left(c-\frac{b^{2}}{4a}\right)=\frac{151}{32},\implies{8}\left(x+\frac{3}{16}\right)^{2}+\frac{151}{32}=8x^2+3x+5. $$