Answer
a) See graph
b) Domain $(-\infty, \infty)$
Range$ [-4, \infty)$
c) Decreasing $(-\infty, 1]$
Increasing $[1, \infty )$
Work Step by Step
$f(x) = x^2 - 2x - 3$
a) $a = 1$, $b = -2$, $c = -3$
a > 0, so graph will open up
vertex $x = \frac{-b}{2a} = 1$
axis of symmetry $x = 1$
Minimum value = $f(1) = 1^2 -2 - 3 = -4$
For x intercept $y = 0$
we get $x^2 - 2x - 3 = 0$
=> $(x-3)(x+1) = 0$
$ x= 3, -1$
y-intercept at $x = 0$, $(0, -3)$
b) Domain $(-\infty, \infty)$
Range$ [-4, \infty)$
c) Decreasing $(-\infty, 1]$
Increasing $[1, \infty )$
