The parabola

The parabola is the first curve we study systematically. Learning to read the graph of $y=ax^2+bx+c$ will be useful both for inequalities and for analytic geometry problems. The chapter starts from the definition of the parabola and the formulae for the vertex, the axis of symmetry and the concavity; it continues with the intersections between a line and a parabola and with the tangency condition ($\Delta=0$); finally it exploits the parabola to draw functions with absolute value and to solve equations and inequalities with absolute values, from the general splitting method up to the cases with two absolute values.

Sections

• Graph of the parabola
• Line–parabola intersections
• Tangent line to the parabola
• Functions with absolute value
• Equations with absolute value
• Inequalities with absolute value

Exercises

• All the worked exercises of the chapter