Math Problem Statement

Gambarlah grafik fungsi f(x) = x²

Solution

It appears that the image shows a mathematical instruction involving the phrase "Gambarlah grafik fungsi f(x) = x²". This translates to "Draw the graph of the function f(x)=x2f(x) = x^2."

The graph of f(x)=x2f(x) = x^2 is a parabola, which opens upwards. Here are some key features of the graph:

  • Vertex: The vertex of the parabola is at (0,0)(0, 0), which is the lowest point since the coefficient of x2x^2 is positive.
  • Axis of symmetry: The graph is symmetric about the y-axis (i.e., the vertical line x=0x = 0).
  • Shape: The parabola gets wider as xx moves away from zero.
  • Intercepts:
    • The y-intercept is f(0)=02=0f(0) = 0^2 = 0.
    • The x-intercepts are also at x=0x = 0, because f(x)=0f(x) = 0 only when x=0x = 0.

Would you like a more detailed breakdown of how to sketch this graph, or any further assistance?

Here are some follow-up questions to explore:

  1. How does the shape of the parabola change for other quadratic functions like f(x)=ax2f(x) = ax^2?
  2. What is the effect of adding or subtracting a constant from f(x)=x2f(x) = x^2, such as f(x)=x2+3f(x) = x^2 + 3?
  3. How does the parabola shift if the function includes a linear term, like f(x)=x2+2xf(x) = x^2 + 2x?
  4. What is the domain and range of f(x)=x2f(x) = x^2?
  5. How do the concepts of vertex and symmetry help in sketching quadratic functions?

Tip: For any quadratic function f(x)=ax2+bx+cf(x) = ax^2 + bx + c, the vertex can be found using x=b2ax = -\frac{b}{2a}.

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Math Problem Analysis

Mathematical Concepts

Quadratic Functions
Graphing
Parabolas

Formulas

f(x) = x²

Theorems

Properties of Parabolas
Symmetry in Quadratic Functions

Suitable Grade Level

Grades 7-9