When Dasha arrives to pick up her 14-month-old son Noe from the day-care center at the end of the day, Noe keeps on playing and hardly notices her. Dasha wonders whether he is securely attached and she turns to you for advice. What does Dasha need to know?

How are we suppose to know this

You're asking in the ap section, so i'll give the ap calculus-style answer. alternatively, you can find the vertex of the parabola and use the "y"-coordinate as the answer.

the maximum height can occur at a critical number, that is, a number  such that  .

the derivative of  can be calculated as follows:



find a value of  that is a zero of the derivative:


this is parabola that is opening downward; we can assume there is a maximum at  .

to find that maximum, calculate  .