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

KS Comments:

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.

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