# How do you solve the equation x^2-2x-1=0 by graphing?

Dec 20, 2016

Solutions are $- \frac{1}{2}$ and $2 \frac{1}{2}$

#### Explanation:

When we draw graph of $y = {x}^{2} - 2 x - 1$,

as a point on $x$-axis means $y = 0$,

intercepts on $x$-axis, give the solution of equation ${x}^{2} - 2 x - 1 = 0$

Now, if $x = 2$, $y = - 1$

if $x = 0$, $y = - 1$

if $x = - 2$, $y = 7$

if $x = 1$, $y = - 2$

if $x = 3$, $y = 2$ and if $x = - 3$, $y = 14$

So joining points $\left\{\begin{matrix}2 & - 1 \\ 0 & - 1 \\ - 2 & 7 \\ 1 & - 2 \\ 3 & 2 \\ - 3 & 14\end{matrix}\right\}$ we get the graph
graph{x^2-2x-1 [-10, 10, -5, 5]}

It shows that intercepts on $x$-axis are $- \frac{1}{2}$ and $2 \frac{1}{2}$

Hence, these are the solutions.