All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
$f(-1.5) = (-1.5)^2 a + (-1.5) b + c = 4.5$

$2.25 a -1.5 b + c = 4.5 \rightarrow (1)$

$f(2.1) = (2.1)^2 a + (2.1) b + c = 3.2$

$4.41 a + 2.1 b + c = 3.2 \rightarrow (2)$

$f(3.4) = (3.4)^2 a + (3.4) b + c = 4.1$

$11.56 a + 3.4b + c = 4.1 \rightarrow (3)$

Using the Graphing Calculator, $a = 0.215, b = -0.490, c = 3.281$

(ii)

$f \prime (x) = 2ax + b > 0$ for f to be increasing

$\therefore, x > 1.14$

Firstly, students must be attentive to leaving the answers to 3 decimal places. For f(x) is an increasing function, we know that implies that $f'(x) > 0.$