Unit 6
The first genuinely curved relationship. The vertex gives a maximum or minimum, which is what makes quadratics useful for modelling.
Lesson 6.1
Choose a method based on the equation structure. Factoring works efficiently when integer factors are visible. Isolating a squared expression supports square roots. The quadratic formula works for every quadratic with nonzero leading coefficient; include both signs when taking square roots.
Lesson 6.2
Vertex form reveals a parabola extremum and axis of symmetry. A positive leading coefficient opens upward and gives a minimum; a negative coefficient opens downward and gives a maximum. In a context, interpret the coordinates using the input and output units and restrict the domain appropriately.
Lesson 6.3
The discriminant is the expression under the square root in the quadratic formula. Its sign determines the number of real roots. A positive nonsquare value gives two irrational real roots; zero gives one repeated real root; a negative value gives no real roots.
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