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

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 $2 {x}^{2} - 13 x - 7 = 0$ can be found by graphing the equation:
$y = 2 {x}^{2} - 13 x - 7$

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

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 $y = 2 {x}^{2} - 13 x - 7$,
find the $x$-intercepts, Those are the solutions to
$2 {x}^{2} - 13 x - 7 = 0$

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 $y = 2 {x}^{2} - 13 x - 7$, (the $x$--intercepts of the graph of $y = 2 {x}^{2} - 13 x - 7$,)
are $= \frac{1}{2}$ and $7$.

Check that

$2 {\left(- \frac{1}{2}\right)}^{2} - 13 \left(- \frac{1}{2}\right) - 7$ and $2 {\left(7\right)}^{2} - 13 \left(7\right) - 7$ give you $0$. (They do.)