\( h(r)=(r+1)(r+8) \) 1) What are the zeros of the function? Write the smaller \( r \) first, and the larger \( r \) secon smaller \( r= \) larger \( r= \) 2) What is the vertex of the parabola? 2

1) To find the zeros of the function h(r) = (r + 1)(r + 8), set the function equal to zero:   (r + 1)(r + 8) = 0 This gives us two equations:   r + 1 = 0  or  r + 8 = 0 Solving each:   r = -1  and  r = -8 The smaller r is -8 and the larger r is -1. smaller r = -8 larger r = -1 2) The vertex of a parabola given in factored form can be found by averaging the zeros (which gives the r-coordinate of the vertex). So:   r-coordinate of vertex = (r₁ + r₂) / 2   = (-8 + (-1)) / 2   = (-9) / 2   = -9/2 To find the y-coordinate of the vertex, substitute r = -9/2 back into the function:   h(-9/2) = (-9/2 + 1) * (-9/2 + 8) Simplify each term:   -9/2 + 1 = -9/2 + 2/2 = -7/2   -9/2 + 8 = -9/2 + 16/2 = 7/2 Now multiply:   (-7/2) * (7/2) = -49/4 Thus, the vertex of the parabola is at:   (-9/2, -49/4)