Step-by-step explanation:
Note that this graph has roots at x = 1 and x = 5. Its maximum occurs at (3, 4) and it opens downward. So writing the vertex form of this graph, we get
[tex]y = - (x - 1)(x - 5)[/tex]
Then expanding this, the equation becomes
[tex]y = - {x}^{2} + 6x - 5[/tex]
As a check, note that the y-intercept is at (0, -5) so if we use x = 0 in the equation above, we see that y = -5. Similarly, if we use x = 3, the value of y is y = 4, as expected.
