Answer
a) See graph
b) Domain $(-\infty, \infty)$
Range$ [0.75, \infty)$
c) Decreasing $(-\infty, 0.25]$
Increasing $[0.25, \infty)$
Work Step by Step
$f(x) = 4x^2 - 2x + 1$
a) $a = 4$, $b = -2$, $c = 1$
a > 0, so graph will open up
vertex $x = \frac{-b}{2a} = 0.25$
axis of symmetry $x = 0.25$
Minimum value = $f(0.25) = 4(0.25)^2 -2 \times 0.25 + 1 = .75$
For x intercept $y = 0$
we get $ 4x^2 - 2x + 1 = 0$
=>Discriminant of quadratic is negative so no intercepts
y-intercept at $x = 0$, $(0, 1)$
b) Domain $(-\infty, \infty)$
Range$ [0.75, \infty)$
c) Decreasing $(-\infty, 0.25]$
Increasing $[0.25, \infty)$
