Fungsi Kuadrat Bagian 2 - Grafik Fungsi Kuadrat Matematika Wajib Kelas X m4thlab

Steps to Sketch a Quadratic Function Graph
📌 The process for graphing a quadratic function $f(x) = ax^2 + bx + c$ involves four main steps, building upon concepts from the first part of the series.
📌 Step 1: Determine the intersection points with the x-axis (by setting $y=0$ or $f(x)=0$) and the y-axis (by setting $x=0$).
📌 Step 2: Find the vertex (turning point or extreme point) using the coordinates $\left(-\frac{b}{2a}, -\frac{D}{4a}\right)$, where $D = b^2 - 4ac$ is the discriminant.
📌 Step 3: Optionally, determine several auxiliary points to help smooth the curve.
📌 Step 4: Connect the resulting points (from steps 1-3) to form a smooth curve.

Example Graphing: $f(x) = x^2 - 2x - 8$
📌 X-intercepts: Setting $y=0$ yields $x^2 - 2x - 8 = 0$, which factors to $(x+2)(x-4)=0$, giving intercepts at (-2, 0) and (4, 0).
📌 Y-intercept: Setting $x=0$ yields $f(0) = -8$, giving the intercept at (0, -8).
📌 Vertex (Turning Point): The x-coordinate is $-\frac{b}{2a} = -\frac{(-2)}{2(1)} = 1$. Substituting $x=1$ gives $y = 1^2 - 2(1) - 8 = 1 - 2 - 8 = -9$. The vertex is (1, -9).
📌 Auxiliary Points: Points like (-1, -5) and (3, -5) were calculated by substituting $x=-1$ and $x=3$ into the function.

Analyzing Coefficients (a, b, c) Influence on the Graph
📌 The coefficient 'a' determines the opening direction: if $a > 0$, the parabola opens upwards; if $a < 0$, it opens downwards.
📌 The coefficient 'c' directly dictates the y-intercept; its value is the y-coordinate where the graph crosses the y-axis.
📌 Determining the sign of 'b' involves an imaginative trick: visualize the graph tipping over its y-intercept. If the resulting tilted curve resembles the less-than sign (<), then $b < 0$. If it resembles the greater-than sign (>), then $b > 0$. If the y-intercept is directly on the axis of symmetry, $b=0$.

Applying Coefficient Analysis to Example Problems
📌 In the first example, where the graph opens downwards ($a < 0$) and leans to the right (implying $b > 0$ based on the tipping analogy), and the y-intercept is negative ($c < 0$), the correct coefficients are $a < 0, b > 0, c < 0$.
📌 For the second example, the graph opens downwards ($a < 0$), the y-intercept is below the x-axis ($c < 0$ or $c < 4$), and the tilt suggests $b > 0$. This matches option B.

Key Points & Insights
➡️ Sketching a quadratic graph requires identifying x and y intercepts and the vertex ($\left(-\frac{b}{2a}, -\frac{D}{4a}\right)$).
➡️ The sign of 'a' determines if the parabola opens up ($a>0$) or down ($a<0$).
➡️ The value of 'c' is the y-coordinate of the y-intercept.
➡️ The sign of 'b' can be estimated by observing the lean of the curve relative to the y-axis using an imaginative tipping analogy to determine if $b$ is positive, negative, or zero.

📸 Video summarized with SummaryTube.com on Feb 03, 2026, 03:12 UTC