# How do find the vertex and axis of symmetry, and intercepts for a quadratic equation  f(x)=-4x^2 ?

$\textcolor{w h i t e}{\text{XXXX}}$$f \left(x\right) = m {\left(x - a\right)}^{2} + b$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$with vertex at $\left(x , f \left(x\right)\right) = \left(a , b\right)$
Since$f \left(x\right) = - 4 {x}^{2}$ can be written
$\textcolor{w h i t e}{\text{XXXX}}$$f \left(x\right) = - 4 {\left(x - 0\right)}^{2} + 0$
it has a vertex at $\left(x , f \left(x\right)\right) = \left(0 , 0\right)$
$f \left(x\right) = - 4 {x}^{2}$ is a parabola which opens downward with an axis of symmetry as vertical line through the vertex.
That is, the axis of symmetry is $x = 0$