Sanai Potter

2023-03-13

How to write $f\left(x\right)=-{x}^{2}+6x-13$ into vertex form?

lilcliffordt42

$\text{the equation of a parabola in}\phantom{\rule{1ex}{0ex}}\text{vertex form}$ is
$\overline{\underline{|\frac{2}{2}y=a{\left(x-h\right)}^{2}+k\frac{2}{2}|}}$
where an is a constant and the vertex's coordinates are (h, k).
$\text{using the method of}\phantom{\rule{1ex}{0ex}}\text{completing the square}$
$f\left(x\right)=-\left({x}^{2}-6x+13\right)$
$f\left(x\right)=-\left({x}^{2}-6x+9-9+13\right)$
$f\left(x\right)=-\left({\left(x-3\right)}^{2}+4\right)$
$f\left(x\right)=-{\left(x-3\right)}^{2}-4←\phantom{\rule{1ex}{0ex}}\text{in vertex form}$

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