How you would solve the following equation #2x^2-13x-7=0# by graphing?

1 Answer
Mar 28, 2015

In order to solve y graphing you need some way of getting a graph without solving the equation. I'll assume that you have computer graphing software (perhaps a computer of a graphing calculator).

Solutions to #2x^2-13x-7=0# can be found by graphing the equation:
#y=2x^2-13x-7#

The solutions to the equation #2x^2-13x-7=0# are exactly the values for #x# that make #y=0# in #y= 2x^2-13x-7#.

On a graph, if a value for #x# makes #y=0#, then we have found an #x#-intercept. (and vice-versa).

So, we want to look at the graph of #y=2x^2-13x-7#,
find the #x#-intercepts, Those are the solutions to
#2x^2-13x-7=0#

Here's the graph. There is no "trace" feature, but you can zoom in using your mouse wheel.

graph{y=2x^2-13x-7 [-11.34, 20.7, -9.46, 6.56]}

If looks like the solutions of #y=2x^2-13x-7#, (the #x#--intercepts of the graph of #y=2x^2-13x-7#,)
are #=1/2# and #7#.

Check that

#2(-1/2)^2-13(-1/2)-7# and #2(7)^2-13(7)-7# give you #0#. (They do.)