What is the discriminant of a quadratic function?

• The discriminant of a quadratic is denoted by the Greek letter Δ (upper case delta)
• For the quadratic function the discriminant is given by
  • • This is given in the?formula booklet
• The discriminant is the expression that is square rooted in the?quadratic formula

How does the discriminant of a quadratic function affect its graph and roots?

Forming equations and inequalities using the discriminant

• Often at least one of the coefficients of a quadratic is?unknown
  • Questions usually use the letter?k?for the unknown constant
• You will be given a fact about the quadratic such as:
  • The?number of solutions?of the equation
  • The?number of roots?of the graph
• To find the?value or range of values?of?k
  • Find an?expression for the discriminant
  • Decide whether Δ > 0, Δ = 0 or Δ < 0
    • If the question says there are?real roots?but does not specify how many then use Δ ≥ 0
  • Solve?the resulting equation or inequality