SOLUTION: without solving the equation or factoring, determine the solution to the equation, x^2+4x-5=0, using only the graph.

Temporarily replace the 0 by . That
sounds like a strange thing to do, but in
the end we will only use the value 0 for y.

 

Calculate this table of points:

 x| y
-6| 7
-4|-5
-2|-9
 0|-5
 2| 7

Plot the points (-6,7), (-4,-5), (-2,-9), (0,-5), (2,7)



Draw a smooth curve through those points moving
from left to right:



Now since we replaced 0 by y in the beginning,
we can only use the part of the graph where
y = 0, and y is 0 only on the x axis.  So we
look to see whene the graph crosses the x-axis.

The points where the graph crosses the x-axis
appear to be (-5,0), and (1,0).

Notice that the y-values are 0 at those points,

so the solutions are  and .

Edwin