Sonia graphs the equations y = –x2 + 4x and y = x – 4 to solve the equation –x2 + 4x = x – what are the solutions of –x2 + 4x = x – 4?

The solutions of the equation is:

               x= -1 and x=4

The solution of the graphs of the equation is equal to the x-value of the point of intersection of the graph of two functions i.e. the function on the left side of the equality on the right side of the equality.

Here, the expression is:

Hence, we will see at which point the graph  of:

and meet.

The point of intersection of the graph is: (-1,-5) and (4,0).

Hence, the solution of the graph is: x= -1 and x=4