Quadratic Functions (Cambridge O Level Additional Maths)

Find the values of the constant  for which the equation  has real roots.

Find the values of for which .

Write  in the form , where , and  are constants.

Hence write down the coordinates of the minimum point of the curve .

Solve .

Find the set of values of  for which  has no real roots.

Solve .

Find the values of  for which the line  is a tangent to the curve .

Find the values of  for which the line  intersects the curve  at two distinct points.

Find the exact values of the constant  for which the line is a tangent to the curve 

Find the values of  for which the line  and the curve  do not intersect.

The curve  intersects the straight line  at two distinct points. Find the possible values of .