A) Draw the graph for the relation y = x2 − 3x − 5 using the interval -3 x 6. From the graph, find the; (i) coordinates at the turning point. (ii) the minimum value (iii) the truthset of y = x2 − 3x -

Note: The graph would be drawn by plotting these points and drawing a smooth curve through them.

The turning point (vertex) of a parabola $y = ax^2 + bx + c$ is at $x = \frac{-b}{2a}$.
For $y = x^2 - 3x - 5$, we have $a=1$, $b=-3$, $c=-5$.

Substitute $x=1.5$ into the equation to find $y$:

(i) The coordinates at the turning point (read from the graph) are approximately $\boxed{(1.5, -7.25)}$.

(ii) The minimum value (read from the graph) is the $y$-coordinate of the turning point: $\boxed{-7.25}$.

The truthset consists of the $x$-intercepts where $y=0$. From the table, $y$ changes from negative to positive between $x=-1$ and $x=0$, and between $x=4$ and $x=5$.
Using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$:

(iii) The truthset of $y = x^2 - 3x - 5 = 0$ (read from the graph) is approximately $\boxed{\{-1.19, 4.19\}}$.

Part 8b:

If the roots are $\alpha$ and $\beta$, the quadratic equation is $x^2 - (\alpha + \beta)x + \alpha\beta = 0$.
Given roots $\alpha = -6$ and $\beta = 13$.
Sum of roots: $\alpha + \beta = -6 + 13 = 7$.
Product of roots: $\alpha\beta = (-6)(13) = -78$.
Substitute these values into the general equation:

The equation is $\boxed{x^2 - 7x - 78 = 0}$.

Question 9:
A total of 50 items consisting of pens and pencils were bought for GH¢190. A pen cost GH¢ and a pencil costs GH¢3.
a. form a linear equation to represent the situation
b. find the number of pen and pencils bought
c. how much will a customer pay for 8 pens and 4 pencils.

Assumption: The cost of a pen is missing from the question. We will assume the cost of a pen is GH¢4.

Let $p$ be the number of pens and $c$ be the number of pencils.
The total number of items is 50:

The cost of a pen is GH¢4 and a pencil is GH¢3. The total cost is GH¢190:

a) The linear equations representing the situation are:
$\boxed{p + c = 50}$
$\boxed{4p + 3c = 190}$

From equation (1), express $c$ in terms of $p$:

Substitute this into equation (2):

Now find $c$:

b) The number of pens bought is $\boxed{40}$ and the number of pencils bought is $\boxed{10}$.

Cost of 8 pens = $8 \times \text{GH¢}4 = \text{GH¢}32$.
Cost of 4 pencils = $4 \times \text{GH¢}3 = \text{GH¢}12$.
Total cost = Cost of 8 pens +