A quadratic function $f$ is given.
$f(x) = -4x^2 - 20x + 1$
(a) Express $f$ in standard form.
f(x) =
(b) Find the vertex and $x$- and $y$-intercepts of $f$. (If an answer does not exist, enter DNE.)
vertex $(x, y) = (?, ?)$
x-intercepts $(x, y) = (?, ?)$ (smaller $x$-value)
$(x, y) = (?, ?)$ (larger $x$-value)
y-intercept $(x, y) = (?, ?)$
(c) Sketch a graph of $f$.