How do you graph Y=x^2+5x+3?

$y = {x}^{2} + 5 x + 3 = {x}^{2} + 2 \frac{5}{2} x + \frac{25}{4} - \frac{13}{4} = \left({x}^{2} + 2 \frac{5}{2} x + \frac{25}{4}\right) - \frac{13}{4}$
$= {\left(x + \frac{5}{2}\right)}^{2} - \frac{13}{4}$
• ${\left(x + \frac{5}{2}\right)}^{2}$ is the parabola graph with vertex: minimum at $\left(- \frac{5}{2} , 0\right)$,
• ${\left(x + \frac{5}{2}\right)}^{2} - \frac{13}{4}$ is the graph of ${\left(x + \frac{5}{2}\right)}^{2}$ shifted $\frac{13}{4}$ points downwards.