A diver jumps upward from the diving board and performs a double twist before entering the water. The function shown describes her height \( h(t) \) in feet above the water, \( t \) seconds after she jumps. \( h(t)=10+32 t-16 t^{2} \) Question: How high will the diver be at the peak of her dive? Enter your final answer rounded to the nearest tenth (one decimal place.) Enter the correct units for your answer in the second box. Answer:

To find the peak height of the diver's dive, we can use the function \( h(t) = 10 + 32t - 16t^2 \). The peak of a quadratic function occurs at the vertex, which can be found using the formula \( t = -\frac{b}{2a} \). Here, \( a = -16 \) and \( b = 32 \). Calculating the time at which the peak height occurs: \[ t = -\frac{32}{2 \times -16} = 1 \text{ second} \] Now, substitute this time back into the height function: \[ h(1) = 10 + 32(1) - 16(1^2) = 10 + 32 - 16 = 26 \text{ feet} \] Thus, the peak height of the diver is **26.0**. **Units:** feet