\( h(t)=-(t-7)^{2}+4 \) 1) What are the zeros of the function? Write the smaller \( t \) first, and the larger \( t \) second. smaller \( t= \) larger \( t= \) 2) What is the vertex of the parabola? a

To find the zeros of the function \( h(t) = -(t-7)^2 + 4 \), set \( h(t) = 0 \): \[ -(t-7)^2 + 4 = 0 \] This leads to: \[ (t-7)^2 = 4 \] Taking the square root gives us: \[ t - 7 = 2 \quad \text{or} \quad t - 7 = -2 \] So, \[ t = 9 \quad \text{and} \quad t = 5 \] Therefore, the smaller \( t \) is: smaller \( t= 5 \) larger \( t= 9 \) Now for the vertex; since it's in the form of \( h(t) = a(t-h)^2 + k \), we see that the vertex form reveals that the vertex, \( (h, k) = (7, 4) \). Hence, the vertex of the parabola is: a \( (7, 4) \)