A parabola is a U-shaped curve that is symmetrical about an axis of symmetry. A quadratic function is of the form f(x)=ax^2+bx+c. The vertex is the turning point where the graph reaches an absolute maximum or minimum
-b/2a represents the x-coordinate of a quadratic function's vertex. The vertex formula is derived from quadratic equations using completing the square method. The vertex coordinates are found using the formula: (h, k) = (-b/2a, (4ac - b^2)/4a)
Inflection point occurs when function changes direction of convexity. Graph passes from one side of tangent line to other at inflection point. Function's graph lies within vertical angles formed by tangent and normal
Concavity describes the direction of a graph's bending. Tangent line lies below graph for concave up, above for concave down. Point of inflection occurs when concavity changes direction
Inflection points occur where concavity changes on a function's graph. To find inflection points, find values where f''(x) = 0 or doesn't exist. Break domain into intervals and evaluate f''(x) at each value. Points where f''(x) changes sign and are in domain are inflection points