Question

What must be true about the discriminant of this quadratic equation for the mentioned values of k? Assume p>0.

Answer 1

1/(4p)(x-h)^2+k=0

1/(4p)(x-h)^2 = -k

k(4p)(x-h)^2+1=0

4kp (x^2 - 2xh + h^2) + 1 = 0

4kp x^2 - 8kph x + 4kph^2+1 = 0

D = (-8kph)^2 - 4(4kp)(4kph^2+1) = 64(kph)^2 - 64(kph)^2 - 16kp
D = -16kp < 0

SO discriminant is always less than 0