Answer
When x = -1.5, y = 5.25
When y = 5, x = -1.62 and 0.62
(i) (-0.5, 6.25)
(ii) x = -0.5
Explanation
From the graph:
When x = -1.5, y = 5.25 (Traced on the graph with red color)
When y = 5, x = -1.62 and 0.62 (Traced on the graph with blue color)
(i) The coordinates of the maximum turning point on the graph is: (-0.5, 6.25) (Traced on the graph with green color).
(ii) To use the formula = -b/2a to justify the x-value at the turning point, we use:
[tex]\begin{gathered} f(x)=-x+6-x^2 \\ \text{from the function,} \\ a=-1,b=-1,\text{ and c }=6 \\ x=\frac{-b}{2a}=\frac{-\mleft(-1\mright)}{2\times(-1)}=\frac{1}{-2}=\frac{-1}{2}=-0.5 \end{gathered}[/tex]
The turning point is justified.
