Fungsi Kuadrat Bagian 1 - Matematika Wajib Kelas X m4thlab

General Concepts of Quadratic Functions
📌 Quadratic functions have a general form: $f(x) = ax^2 + bx + c$, where $a \neq 0$.
📌 The graph of a quadratic function is a parabola, similar to the shapes seen in structures like the Gateway Arch or Harbour Bridge.
📌 The direction the parabola opens depends on the coefficient '$a$': if $a > 0$, it opens upwards; if $a < 0$, it opens downwards.

Identifying Coefficients and Intercepts
📌 Coefficients $a$, $b$, and $c$ must be correctly identified from the equation (e.g., in $y = 3x^2 - 2x + 1$, $a=3$, $b=-2$, $c=1$).
📌 To find the x-intercepts, set $f(x) = 0$ and solve the resulting quadratic equation, yielding points $(x, 0)$.
📌 To find the y-intercept, set $x = 0$, which simplifies to $f(0) = c$, yielding the point $(0, c)$.

Vertex, Axis of Symmetry, and Extrema
📌 The vertex (or turning point) of the parabola has coordinates $(x_p, y_p)$.
📌 The x-coordinate of the vertex (abscissa) is calculated using the formula $x_p = -\frac{b}{2a}$.
📌 The y-coordinate of the vertex (ordinate) is calculated using $y_p = -\frac{D}{4a}$, where $D = b^2 - 4ac$ (the discriminant).
📌 The axis of symmetry is the vertical line passing through the vertex, given by the equation $x = x_p = -\frac{b}{2a}$.
📌 The function has a maximum value if the parabola opens down ($a < 0$, value is $y_p$), or a minimum value if it opens up ($a > 0$, value is $y_p$).

Domain and Range from Graphs
📌 The Domain (Daerah Asal) refers to the set of all possible $x$ values. If there are no explicit boundaries (indicated by arrows), the domain is often all real numbers ($\mathbb{R}$).
📌 The Range (Daerah Hasil) refers to the set of all possible $y$ values, determined by the minimum or maximum $y$ value (the vertex's $y$-coordinate). For example, if the minimum $y$ is $-1$, the range is $y \geq -1$.

Key Points & Insights
➡️ Mastering coefficient identification ($a, b, c$) is crucial as these values are foundational for all subsequent calculations (vertex, intercepts, etc.).
➡️ When finding the y-intercept, the constant term $c$ directly gives the y-coordinate $(0, c)$, which is the quickest method.
➡️ Remember the mnemonic for the vertex coordinates: $\left( -\frac{b}{2a}, -\frac{D}{4a} \right)$, which is described as "Mimin berduaan di perempatan" (Mimin together at the intersection/crossroads).
➡️ To determine if the extremum is a maximum or minimum, check the sign of $a$: $a > 0$ means minimum (opens up); $a < 0$ means maximum (opens down).

📸 Video summarized with SummaryTube.com on Feb 03, 2026, 03:09 UTC