What is the maximum height attained by an object with the height equation h = 10t – 5t²?

To find the maximum height attained by the object, we first need to analyze the height function:

h(t) = 10t – 5t²

This is a quadratic equation where a = -5, b = 10, and c = 0. The maximum point of a quadratic equation occurs at the vertex, which can be found using the formula:

t_{vertex} = -\frac{b}{2a}

Substituting the values in:

t_{vertex} = -\frac{10}{2 \times -5} = \frac{10}{10} = 1 ext{ second}

Now that we have the time at which the maximum height occurs, we can plug this value back into the height equation to find h:

h(1) = 10(1) – 5(1)² = 10 – 5 = 5 ext{ meters}

Thus, the maximum height attained by the object is 5 meters.