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?

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Answer 1 · 2015-05-17T20:40:14

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

$x_{v}$ $x_v$ = $- \frac{b}{2 a}$ $- b / (2 a)$ and $y_{v}$ $y_v$ = $- Delta / (4 a)$ , 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 $(y = x^2 - 10 x)$ , the coordinates of the vertex will be:

$x_v = - (-10)/2$ $=$ $5$

$y_v = -(100/4)$ $=$ $-25$

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