Solving Quadratic Equations - By Graphing

Example: $2x^2 -4x =6$

Step 1: Put all terms on the same side of the equation (Solve for zero)

$2x^2-4x-6=0$

Step 2: Replace the zero with a y

$2x^2-4x-6=y$

Step 3: Make an input/output table

x $2x^2-4x-6$ y
-2 $2(-2)^2 - 4(-2) -6$ 10
-1 $2(-1)^2 - 4(-1)-6$ 0
0 $2(0)^2 - 4(0) -6$ -6
1 $2(1)^2 - 4(1) -6$ -8
2 $2(2)^2 - 4(2) -6$ -6

Step 4: Graph the points
(-2,10)
(-1,0)
(0, -6)
(1, -8)
(2, -6)

Step 5: Estimate the points where the line crosses the x-axis. These are the solutions to the original equation.

Solutions: x= -1, x = 3

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