BIG IDEAS Standard Form of a Quadratic: Quadratic Formula: Discriminant = Analyzing the Discriminant The discriminant can be used to determine the number of and type of solutions to a quadratic equation. Every quadratic can have zero, one, or two solutions. Solutions can be real or imaginary numbers. If the Value of the Characteristics and Examples Discriminant Is: Number of Solutions of the Quadratic Equation Are: If the value of the discriminant is Negative negative, then there will be two imaginary number solutions and no x-axis intercepts. If the value of the discriminant is zero, then there will be one Zero real solution and the graph will touch the at one and only one point. If the value of the Positive discriminant is a Perfect Square positive perfect square, then there will be two integer solutions and two x-axis intercepts. If the value of the discriminant is positive, Positive Not a Perfect Square but not a perfect square,
BIG IDEAS Standard Form of a Quadratic: Quadratic Formula: Discriminant = Analyzing the Discriminant The discriminant can be used to determine the number of and type of solutions to a quadratic equation. Every quadratic can have zero, one, or two solutions. Solutions can be real or imaginary numbers. If the Value of the Discriminant Is: Characteristics and Number of Solutions of the Quadratic Equation Are: Examples Negative If the value of the discriminant is negative, then there will be two imaginary number solutions and no x-axis intercepts. Zero If the value of the discriminant is zero, then there will be one real solution and the graph will touch the at one and only one point. Positive Perfect Square If the value of the discriminant is a positive perfect square, then there will be two integer solutions and two x-axis intercepts. Positive Not a Perfect Square If the value of the discriminant is positive, but not a perfect square,
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