Calculus with Applications (10th Edition)

$\left(-\displaystyle \frac{3}{2}, -\displaystyle \frac{7}{4}\right)$.
$f(x)=a(x-h)^{2}+k^{2},\qquad$ vertex: (h,k) (solved as in example 4) $(A\pm B)^{2}=A^{2}\pm 2AB+B^{2}$ ----------- $y=3x^{2}+9x+5$ $=3(x^{2}+3x)+5$ $=3(x^{2}+2\displaystyle \cdot\frac{3}{2}\cdot x+\frac{9}{4}-\frac{9}{4})+5$ $=3(x^{2}+3x+\displaystyle \frac{9}{4})+5-3(\frac{9}{4})$ $=3(x+\displaystyle \frac{3}{2})^{2}-\frac{20-27}{4}$ $=3(x+\displaystyle \frac{3}{2})^{2}-\frac{7}{4}$ Vertex: $(-\displaystyle \frac{3}{2}, -\displaystyle \frac{7}{4})$.