Question

the graph of $y = -x^2 + 4x$ is shown below. use the graph to solve the equation $-x^2 + 4x = 0$.
enter the solution(s) in the box below. if there is more than 1 solution, separate the values with a comma (example: -3, 2). if there are no solutions, enter dne for does not exist.

Explanation:

Step1: Identify equation goal

We need to solve $-x^2 + 4x = 0$, which is equivalent to finding where $y=-x^2+4x$ intersects $y=0$ (the x-axis).

Step2: Find x-intercepts from graph

The graph crosses the x-axis at $x=0$ and $x=4$. We can verify algebraically:
Factor the equation:
$$-x(x - 4) = 0$$
Set each factor to 0:
$-x=0 \implies x=0$
$x-4=0 \implies x=4$

Answer:

0, 4