PDF chapter test TRY NOW

5. Examples of solving quadratic equations through intersection of lines

Let us learn how to graphically solve

$2$ quadratic equations.

Example:

1. Draw the graph of

$y = x^2 + 2x - 3$ and hence solve

$x^2 - x - 6 = 0$ .

Solution:

Step 1: Draw the graph of the equation

$y = x^2 + 2x - 3$ .

The table of values for the equation

$y = x^2 + 2x - 3$ is given by:

$x$	$-4$	$-3$	$-2$	$-1$	$0$	$1$	$2$
$y$	$5$	$0$	$-3$	$-4$	$-3$	$1$	$5$

Step 2: To solve the equation

$x^2 - x - 6 = 0$ , subtract the equation

$x^2 - x - 6 = 0$ from

$y = x^2 + 2x - 3$ .

$y = x^2 + 2x - 3$

$0 = x^2 - x - 6$ (

$-$ )

-----------------------------

$y = x + 3$

-----------------------------

Step 3: Draw the graph of the equation

$y = x + 3$ .

The table of values for the equation

$y = x + 3$ is given by:

$x$	$-4$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$
$y$	$-1$	$0$	$1$	$2$	$3$	$4$	$5$	$6$

Step 4: Mark the points of intersection of

$y = x^2 + 2x - 3$ and

$y = x + 3$ . The point of intersection is

$(-3,0)$ and

$(2,5)$ .

Step 5: The

$x$ - coordinates of the points are

$-3$ and

$2$ . Therefore, the solution set for the equation

$x^2 - x - 6 = 0$ is

${-3,2}$ .

2. Draw the graph of

$y = 2x^2 + x - 2$ and hence solve

$2x^2 = 0$ .

Step 1: Draw the graph of the equation

$y = 2x^2 + x - 2$ .

The table of values for the equation

$y = 2x^2 + x - 2$ is given by:

$x$	$-2$	$0$	$2$
$y$	$4$	$-2$	$8$

Step 2: To solve the equation

$2x^2 = 0$ , subtract

$2x^2 = 0$ from

$y = 2x^2 + x - 2$ .

$y = 2x^2 + x - 2$

$0 = 2x^2$ (

$-$ )

-------------------------------

$y = x - 2$

-------------------------------

Step 3: Draw the graph of the equation

$y = x - 2$ .

The table of values for the equation

$y = x - 2$ is given by:

$x$	$-2$	$-1$	$0$	$1$	$2$	$3$
$y$	$-4$	$-3$	$2$	$-1$	$0$	$1$

Step 4: Mark the points of intersection of

$y = 2x^2 + x - 2$ and

$y = x - 2$ . The point of intersection is

$(0,-2)$ .

Step 5: The

$x$ - coordinates of the points is

$0$ . Therefore, the solution set for the equation

$2x^2 = 0$ is

$0$ .

Previous theory

Exit to the topic

Did you find an error?

Register for free to see more content

Register for free to see more content