5. STORAGE The front of a storage bunker can be modeled by \( y=-\frac{5}{216}(x-72)(x+72) \), where \( x \) and \( y \) are measured in inches. The \( x \)-axis represents the ground. Find the width of the bunker at ground level. (Section 7.5 )

To find the width of the bunker at ground level, we need to determine where the front of the storage bunker intersects the ground, which is represented by \( y = 0 \). We set the equation \( y = -\frac{5}{216}(x-72)(x+72) \) equal to zero: \[ -\frac{5}{216}(x-72)(x+72) = 0 \] This implies that either \( (x-72) = 0 \) or \( (x+72) = 0 \). Solving these, we find: 1. \( x - 72 = 0 \) leads to \( x = 72 \) 2. \( x + 72 = 0 \) leads to \( x = -72 \) The total distance between these two points is: \[ 72 - (-72) = 72 + 72 = 144 \text{ inches} \] So, the width of the bunker at ground level is **144 inches**. To further verify, you could check that the function \( y \) equals zero at these points, reaffirming that they mark the width of the structure. Always remember, when you set a quadratic equation to zero, finding the x-intercepts will lead you right to the necessary dimensions!