The formula y=0.4x2-36x+1000 models the number of accidents, y, per 100 millions miles driven, for drivers x years old, where 20 < x< 50.Find the coordinates of the graph’s vertex and describe what this represent in practical terms. Discuss your solution with your team.

I suggest you plot this function and see where the vertex is. Or else find where the derivative dy/dx is equal to zero. Or else just "know" that the x coordinate of the vertex for the parabola y = ax^2 + bx + c is at x = -b/2a.

In more theorical terms, you could complete the square to find the coordinates of the vertex. You will then see that the x coordinates of the vertex becomes x = -b/2a

One other method is using the symmetrical property of the graph. You factor the quadratic, and find the roots. The x coordinate of the vertex is also the x coordinate of the midpoint between the two roots.

The y coordinates of the vertex can then be easily worked out.

If you can plot, or visualise, or sketch the curve representing the quadratic, this will definitely help you in describing what happens to the relationship between the distance covered and the number of accidents.