**Updated on April 16th, 2012: Added a video explanation**

The table below shows corresponding values of \(x\) and \(y\) for the function \(y = x^2 – 2x – 3\), for integer values of \(x\) from -2 to 4.

For **part (a)**, we need to find the value of \(y\) when \(x = -1\) and when \(x = 2\).

When \(x= -1\),

$$

\begin{eqnarray}

y &=& (-1)^2 – 2(-1) – 3 \\

&=& 1 + 2 – 3 \\

&=& 0.

\end{eqnarray}

$$

When \(x= 2\),

$$

\begin{eqnarray}

y &=& (2)^2 – 2(2) – 3 \\

&=& 4 + 4 – 3 \\

&=& -3.

\end{eqnarray}

$$

In **part (b)** we are asked plot the points whose \(x\) and \(y\) values are recorded in the table above, and to draw a smooth curve through the points. The graph below uses a scale of 2 cm to represent 1 unit on the \(x\)-axis, and 1 cm to represent 1 unit on the \(y\)-axis.

For **part (c)**, using the graph we estimate that the value of \(y\) when \(x = 3.5\) is approximately \(2.2\) (**N.B.** The exact answer is \(y = 2.25\)).

Finally, in **part (d)** we make the following observations:

- The equation of the axis of symmetry of the graph is \(x = 1\).
- \(-4\) is the minimum value of the function \(y\).
- When \(x^2 – 2x – 3 = 0\), i.e. \(y = 0\) then from the table we see that \(x = -1\) or \(x = 3\).