Grafik Fungsi Kuadrat Matematika SMP

Introduction

In this tutorial, we will explore how to create and interpret the graph of a quadratic function, a fundamental topic in middle school mathematics. Understanding quadratic functions is crucial for solving various mathematical problems and is applicable in real-world scenarios such as physics, engineering, and economics.

Step 1: Understanding Quadratic Functions

Quadratic functions can be expressed in the standard form:

• f(x) = ax² + bx + c
  • a determines the direction of the parabola (upward if a > 0 and downward if a < 0).
  • b affects the position of the vertex.
  • c is the y-intercept of the graph.

Practical Tip

To identify the characteristics of the quadratic function quickly:

• Check the sign of a to determine the direction.
• Use c to find where the graph intersects the y-axis.

Step 2: Finding the Vertex

The vertex of a quadratic function is its maximum or minimum point and can be found using the formula:

• x = -b / (2a)
• Substitute this value back into the function to find the corresponding y-coordinate.

Example

For the function f(x) = 2x² + 4x + 1:

1. Calculate x:
   • x = -4 / (2 * 2) = -1
2. Find y:
   • f(-1) = 2(-1)² + 4(-1) + 1 = -1

Thus, the vertex is at (-1, -1).

Step 3: Finding the X-Intercepts

To find the x-intercepts (where the graph crosses the x-axis), set f(x) = 0 and solve for x. This can be done using the quadratic formula:

• x = (-b ± √(b² - 4ac)) / (2a)

Practical Advice

• Make sure to check the discriminant (b² - 4ac) to determine the nature of the roots:
  • If positive, there are two distinct real roots.
  • If zero, there is one real root (the vertex).
  • If negative, there are no real roots.

Step 4: Plotting the Graph

Once you have the vertex and x-intercepts, you can plot the graph:

• Start by marking the vertex on the graph.
• Mark the x-intercepts.
• Draw the axis of symmetry, which is the vertical line through the vertex.
• Sketch the parabola opening in the direction determined by a.

Common Pitfall

Avoid making the parabola too steep or too flat. Ensure it reflects the value of a accurately.

Step 5: Analyzing the Graph

After plotting, analyze the graph for:

• The vertex location.
• The direction of opening.
• The intercepts.
• Any symmetry about the vertex.

Real-World Application

Quadratic functions can model various phenomena such as projectile motion, where the path of an object is parabolic.

Conclusion

In this tutorial, we learned how to graph a quadratic function by understanding its components, finding the vertex and x-intercepts, and plotting the graph. Mastering these steps will help you solve quadratic equations and apply this knowledge in real-world situations. Practice with different quadratic functions to strengthen your understanding and skills.