Unit 6 · Core unit
The first genuinely curved relationship. The vertex gives a maximum or minimum, which is what makes quadratics useful for modelling.
What a strong answer looks like
A strong answer says which solving method fits and interprets the vertex in the language of the situation.
Know
Factoring is fastest when it works, square roots suit an isolated square, and the quadratic formula always works.
Apply
Try factoring briefly, then move to the formula rather than persisting.
Watch out
Forcing a factorisation that does not exist over the integers.
Study move
Solve the same equation by two methods and compare.
Know
The vertex is the maximum when the leading coefficient is negative and the minimum when positive, and its input is midway between the zeros.
Apply
Locate the vertex from the axis of symmetry, then evaluate to get its output.
Watch out
Reporting the input of the vertex as the maximum value, when the maximum is the output.
Study move
Find the vertex of a projectile model and state both coordinates with units.
Know
The discriminant reveals how many real solutions exist without solving: positive gives two, zero gives one, negative gives none.
Apply
Compute it first when the question asks only how many solutions there are.
Watch out
Concluding no solution exists at all when only the real solutions vanish.
Study move
Use the discriminant to classify three equations without solving them.
Modeling drill
For a height model, find the maximum height, the time it occurs, and when the object lands, with units throughout.
