# How do you write the vertex form equation of the parabola F(x)=x^2-4x-7?

$F \left(x\right) = {\left(x - 2\right)}^{2} - 11$
vertex form Equation of the Parabola is $y = a {\left(x - h\right)}^{2} + k$
$F \left(x\right) = {x}^{2} - 4 x - 7$
$= {x}^{2} - 4 x + 4 - 4 - 7$
$= {\left(x - 2\right)}^{2} - 11$
This is the vertex form Equation of the Parabola $F \left(x\right)$ where $h = 2$ and $k = - 11$ and Parabola opens $u p$ since $a = 1$ is positive