Answer
a) See graph
b) Domain $(-\infty, \infty)$
Range$ [0, \infty)$
c) Decreasing $(-\infty, -1]$
Increasing $[-1, \infty)$
Work Step by Step
$f(x) = x^2 + 2x + 1 = (x+1)^2$
a) $a = 1$, $b = 2$, $c = 1$
a > 0, so graph will open up
vertex $x = \frac{-b}{2a} = -1$
axis of symmetry $x = -1$
Minimum value = $f(-1) = (-1)^2 -2 +1 = 0$
For x intercept $y = 0$
we get $ x^2 + 2x + 1 = (x+1)^2 = 0$
=> $ x= -1$
y-intercept at $x = 0$, which is $(0, 1)$
b) Domain $(-\infty, \infty)$
Range$ [0, \infty)$
c) Decreasing $(-\infty, -1]$
Increasing $[-1, \infty)$