(Solved): A quadratic relation has an equation of the form \( y=a(x-r)(x-s) \). Determine the value of \( a \ ...

A quadratic relation has an equation of the form \( y=a(x-r)(x-s) \). Determine the value of \( a \) when a) the parabola has zeros at \( (4,0) \) and \( (2,0) \) and a \( y \)-intercept at \( (0,1) \) b) the parabola has \( x \)-intercepts at \( (4,0) \) and \( (-2,0) \) and a \( y \)-intercept at \( (0,-1) \) c) the parabola has zeros at \( (5,0) \) and \( (0,0) \) and a minimum value of \( -10 \) d) the parabola has \( x \)-intercepts at \( (5,0) \) and \( (-3,0) \) and a maximum value of 6 e) the parabola has its vertex at \( (5,0) \) and a \( y \)-intercept at \( (0,-10) \)