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

(i)
At $(1.6, -2.4), ~0.390625a + 1.6b + c = -2.4 \rightarrow (1)$

At $(-0.7, 3.6), ~\frac{1}{0.7^2}a - 0.7b + c = 3.6 \rightarrow (2)$

$\frac{dy}{dx}|_{x=1} = 2$

$\Rightarrow -2a + b = 2 \rightarrow (3)$

Using GC, $a \approx -3.593, b \approx -5.187, c \approx 7.303$ (to 3 decimal place)

(ii)
Using GC, $x = -0.5890038 \approx -0.589$ (to 3 decimal place)

(iii)
$y = -5.19x +7.30$ (to 3 sig fig)