\( f(r)=r^{2}+4 r-60 \) 1) What are the zeros of the function? Write the smaller \( r \) first, and the larger \( r \) second. smaller \( r= \) larger \( r= \) 2) What is the vertex of the parabola? (

To find the zeros of the function \( f(r)=r^{2}+4r-60 \), we can use the quadratic formula \( r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 4 \), and \( c = -60 \). First, calculate the discriminant: \[ b^2 - 4ac = 4^2 - 4(1)(-60) = 16 + 240 = 256. \] Now use the quadratic formula: \[ r = \frac{-4 \pm \sqrt{256}}{2(1)} = \frac{-4 \pm 16}{2}. \] Calculating the two possible values for \( r \): 1. \( r = \frac{12}{2} = 6 \) 2. \( r = \frac{-20}{2} = -10 \) So the zeros of the function are: smaller \( r= -10 \) larger \( r= 6 \) To find the vertex of the parabola, we use the formula \( r = -\frac{b}{2a} \): \[ r = -\frac{4}{2 \cdot 1} = -2. \] Now we can find the corresponding \( f(-2) \): \[ f(-2) = (-2)^{2} + 4(-2) - 60 = 4 - 8 - 60 = -64. \] Thus, the vertex of the parabola is: \( (-2, -64) \).