2. Quadratic functions

• find the maximum or minimum value of the quadratic function f : x ↦ ax 2+ bx + c by any method
• use the maximum or minimum value of f(x) to sketch the graph or determine the range for a given domain
• know the conditions for f(x) = 0 to have:
(i) two real roots, (ii) two equal roots, (iii) no real roots and the related conditions for a given line to
(i) intersect a given curve, (ii) be a tangent to a given curve, (iii) not intersect a given curve
• solve quadratic equations for real roots and find the solution set for quadratic inequalities