What is the formula to find the roots of a quadratic equation ax² + bx + c = 0?

The discriminant D is calculated as ___ and helps determine the nature of roots.

D = b² – 4ac

If the discriminant D is less than 0, the quadratic equation has ___ roots.

Two complex conjugate roots

The vertex of the parabola described by ax² + bx + c can be found at the coordinates ___ and ___.

For the quadratic function f(x) = ax² + bx + c, the axis of symmetry is given by the line ___.

X = -b/(2a)

Given roots α and β, the quadratic equation can be formed as ___ using the sum and product of roots.

X² - (α + β)x + (α × β) = 0

If a > 0 in the quadratic function f(x) = ax² + bx + c, the extremum is a ___ value.

Minimum

For the function y = ax², shifting the graph right by h and up by k results in the equation ___ and ___.

Y = a(x - h)² and y = ax² + k