Question

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

Answer 1

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.)