# How do I use the vertex formula to determine the vertex of the graph for f(x) = 2x^2 − 3x + 8?

May 11, 2015

$\left(- \frac{b}{2} a\right) = \frac{3}{4}$

$f \left(\frac{3}{4}\right) = 2 \left(\frac{9}{16}\right) - 3 \left(\frac{3}{4}\right) + 8 = \frac{55}{8}$

Vertex form:$f \left(x\right) = 2 {\left(x - \frac{3}{4}\right)}^{2} + \frac{55}{8}$

Check:
Develop: 2(x^2 - 3x/2 + 9/16) + 55/8 = 2x^2 - 3x + 9/8 + 55/8

= 2x^2 - 3x + 8