# How do you find the vertex of h(x) + 3/16x^2 - 5/8x - 1/2?

Feb 28, 2016

${x}_{\text{vertex}} = \frac{5}{3}$

I have left ${y}_{\text{vertex}}$ for you to derive by substitution.

#### Explanation:

Quick method: Find ${x}_{\text{vertex}}$ then substitute it back into the original equation to find ${y}_{\text{vertex}}$

Given:$\text{ } \frac{3}{16} {x}^{2} - \frac{5}{8} x - \frac{1}{2}$ ............................(1)

'~~~~~~~~~~~~ For reference: ~~~~~~~~~~~~~~~~~
$\textcolor{b r o w n}{\frac{3}{16} \times k = \frac{5}{8}} \to \textcolor{g r e e n}{k = \frac{5}{8} \times \frac{16}{3} = \frac{10}{3}}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Write equation (1) as:

$\frac{3}{16} \left({x}^{2} \textcolor{g r e e n}{- \frac{10}{3}} x\right) - \frac{1}{2}$

$\textcolor{b l u e}{{x}_{\text{vertex}} = \left(- \frac{1}{2}\right) \times \left(- \frac{10}{3}\right) = + \frac{10}{6} = + \frac{5}{3} = 1.6667}$