Question

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

Answer 1

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 = 2x - x^2`

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

From the graph the x-intercepts are: `(0,0) " & " (2, 0)`

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