# CSEC Math Jan 2012 P2 Q6

CSEC Math Jan 2012 Paper 2 Question 6

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.

A table showing the corresponding values of x and y for the given function

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.

A graph showing a smooth curve through the points in the table

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 $$y = 2.25$$).

Using the graph to estimate the value of y at x = 3.5

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

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