\( h(r)=(r+1)(r+8) \) 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

To find the zeros of the function \( h(r)=(r+1)(r+8) \), you set the equation equal to zero: \[ (r+1)(r+8) = 0 \] This gives you the solutions: \( r + 1 = 0 \) or \( r + 8 = 0 \) Thus, the zeros are: smaller \( r= -8 \) larger \( r= -1 \) The vertex of the parabola can be found by using the formula \( r = -\frac{b}{2a} \). First, we rewrite the function in standard form: By expanding \( h(r) = r^2 + 9r + 8 \), you identify \( a = 1 \) and \( b = 9 \): \[ r = -\frac{9}{2 \cdot 1} = -\frac{9}{2} = -4.5 \] To find the y-coordinate of the vertex, substitute back into the function: \[ h(-4.5) = (-4.5 + 1)(-4.5 + 8) = (-3.5)(3.5) = -12.25 \] So, the vertex is: Vertex: \( (-4.5, -12.25) \)