# How do I use the vertex formula to determine the vertex of the graph of the function and write it in standard form for f(x)=x^2-10x?

May 17, 2015

The vertex formula for a quadratic equation $a {x}^{2} + b x + c$ $=$ 0 is the following:

${x}_{v}$ = $- \frac{b}{2 a}$ and ${y}_{v}$ = $- \frac{\Delta}{4 a}$, where $\Delta = {b}^{2} - 4 a c$

In other words, the vertex is the point $V$ (- b / (2 a); - Delta / (4 a))

in our particular case $\left(y = {x}^{2} - 10 x\right)$, the coordinates of the vertex will be:

${x}_{v} = - \frac{- 10}{2}$$=$ $5$

${y}_{v} = - \left(\frac{100}{4}\right)$$=$$- 25$

Therefore, the vertex is the point $V$(5; -25)