# How do you solve y = 2x - x^2 graphically?

Apr 20, 2017

Graph the function and find the x-intercepts. The x-values of the x-intercepts are the solution. If their are no x-intercepts, there are no solutions.
$x = 0 , x = 2$

#### Explanation:

Given: $y = 2 x - {x}^{2}$

This equation is a parabola:
graph{2x-x^2 [-10, 10, -5, 5]}

From the graph the x-intercepts are: $\left(0 , 0\right) \text{ & } \left(2 , 0\right)$

This means the solutions to the equation are the $x$ values of the $x$-intercepts: $x = 0 , x = 2$