3. A quadratic relation has an equation of the form \( y=a(x-r)(x-s) \). The graph of the relation has zeros at \( (2,0) \) and \( (-6,0) \) and passes through the point \( (3,5) \). Determine the value of \( a \).

To find the value of \( a \), we first identify the roots \( r \) and \( s \) from the zeros given. We have \( r = 2 \) and \( s = -6 \), so the quadratic equation can be written as: \[ y = a(x - 2)(x + 6) \] Now, we need to find \( a \) using the point \( (3, 5) \). We can substitute \( x = 3 \) and \( y = 5 \) into the equation: \[ 5 = a(3 - 2)(3 + 6) \] This simplifies to: \[ 5 = a(1)(9) \] Therefore, we have: \[ 5 = 9a \] Now, we can solve for \( a \): \[ a = \frac{5}{9} \] So, the value of \( a \) is \( \frac{5}{9} \).