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Theory:

Let us learn how to solve \(2\) quadratic equations graphically.
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 \(y = x^2 + 2x - 3\).
 
\(y = x^2 + 2x - 3\)
 
\(0 = x^2 -   x - 6\)  (\(-\))
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\(y = x + 3\)
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Step 3: Draw the graph of the equation \(y = x + 3\).
 
The table of values for the equation \(y = x + 3\) is given by:
 
\(x\)\(-4\)\(-3\)\(-2\)\(-1\)\(0\)\(1\)\(2\)\(3\)
\(y\)\(-1\)\(0\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)
 
6.png
 
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 \(y = 2x^2 + x - 2\).
 
\(y = 2x^2 + x - 2\)
 
\(0 = 2x^2\)             (\(-\))
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\(y = x - 2\)
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Step 3: Draw the graph of the equation \(y = x - 2\).
 
The table of values for the equation \(y = x - 2\) is given by:
 
\(x\)\(-2\)\(-1\)\(0\)\(1\)\(2\)\(3\)
\(y\)\(-4\)\(-3\)\(2\)\(-1\)\(0\)\(1\)
 
7.png
 
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 \(0\).