Vértice na Geometria e na Álgebra: Conceitos e Fórmulas

Section role: supports the 'Vértices em Foco: Geometria de Ângulos e a Curva da Parábola' section while the teacher explains the formal definition of vertex in angles and quadratic functions. Slides: (1) Title — 'O Vértice: Geometria e Funções'; (2) O Vértice nos Ângulos — bullets: definition as the common origin of two rays, visual example of an angle formed by rays, vocabulary 'origem' and 'lados'; (3) Ângulos Opostos pelo Vértice (OPV) — bullets: intersection of two lines, geometric proof of equality, diagram showing opposite angles; (4) Transição para a Álgebra — connection back to Section 1 highlighting that vertex also means turning point, introducing the parabola in $y = ax^2 + bx + c$; (5) O Vértice da Parábola — bullets: definition as the inflection point of the curve, distinction between maximum point (when a < 0) and minimum point (when a > 0); (6) Fórmulas do Vértice — bullets: presentation of formulas $x_v = -b/2a$ e $y_v = - floor/4a$, explanation of the discriminant delta; (7) Exemplo Prático — bullets: step-by-step calculation of the vertex for the function $f(x) = x^2 - 6x + 5$, sketching the parabola on a coordinate plane; (8) Equívoco Comum — warning about confusing the vertex coordinates with the roots of the function (x-intercepts); (9) Fechamento — question: 'Como podemos usar as coordenadas do vértice para encontrar o valor máximo de uma trajetória?' — sets up the calculation and consolidation exercises in Section 3.