Question

Write the quadratic equation that is represented by the graph.​

Answer 1

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

`y = - (x - 1)(x - 5)`

Then expanding this, the equation becomes

`y = - {x}^(2) + 6x - 5`

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.