Question

Draw the graph $y=x^2-9$ and hence solve the equation $x^2-2x-8=0$

Answer 1

To draw the graph, consider the following table.

$\begin{array}{ccccc}x& 3& -3& 0& 4\\ y& 0& 0& -9& 7\end{array}$

Scale: x –axis 1 cm = 1 unit

y – axis 1 cm = 1 unit

The curve, thus obtained is the graph of parabola $y=x^2-9$

Now, solving the equations $y=x^2-9$and $y=x^2-2x-8=0$

We get, y = 2x -1

Now, consider the table for straight line y = 2x -1

$\begin{array}{ccccc}x& 1/2& 0& 1& -1\\ y& 0& -1& 1& -3\end{array}$

Scale: x-axis 1 cm = 4 units; y-axis 1 cm = 4 units

The point of intersection of the parabola and the straight line are (-4, 5) and (2,-5)

The x – coordinates of the points are {-4,2}

Hence, the solution set of the equation $y=x^2-2x-8=0$ = 0 is {-4,2}