Question

How do you solve `x^2+8x-5=0` graphically?

Answer 1

Plot points and identify where the parabola hits the `x` axis

`x=-8.5826` and `x=0.5826`

Explanation:

First, plotting some points, gives

![Desmos.com]()

These points reveal the general shape of the graph.

![Desmos.com]()

Sketching reveals that the solution is around `x~~-8.5` and `x~~0.5`. However, the exact zero still isn't known because of inaccuracies in sketching.

![Desmos.com]()

Finding the exact roots, or zeroes of this equation requires and algebraic solution. Using the quadratic equation gives

`x=(-8+-sqrt((8)^2-4(1)(-5)))/(2(1))`

`x=(-8+-sqrt(84))/2`

`x=(-8+-2sqrt(21))/2`

`x=-8/2+-2sqrt(21)/2`

`x=--4+-sqrt(21)`

`x=-8.5826` and `x=0.5826`