Cara Menggambar Grafik Fungsi Kuadrat

>Hello Sohib EditorOnline, in this journal article, we will discuss how to draw the graph of quadratic function in a relaxed Indonesian language. The quadratic function is a mathematical function which can be represented by a second-degree polynomial equation. The equation of the quadratic function is y = ax² + bx + c. Here, a, b and c are constants and x is a variable. In this article, we will explore how to plot a quadratic function on a graph step by step.

Step 1: Understanding the Basic Concept

Before we start drawing the graph of a quadratic function, it is important to have a basic understanding of the concept. A quadratic function is a parabolic curve. The graph of a quadratic function is a U-shaped curve called a parabola. We can define the shape of the parabola by analyzing the value of the coefficient a in the quadratic equation.

If a is positive, then the parabola opens upward. If a is negative, then the parabola opens downward. Also, the vertex of the parabola is the point where it changes its direction. The vertex lies on the axis of symmetry, which is the vertical line that passes through the vertex.

Now, we are ready to draw the graph of a quadratic function.

Step 2: Computing the Function Values

The first step in drawing a quadratic function graph is to compute the function values for different values of x. To create a graph, we must have a minimum of two points. A quadratic function can have several points, but for simplicity, we will consider two points. We can find these points easily by substituting different values of x to the given quadratic equation.

For example, let’s consider the quadratic equation y = 2x² – 4x + 1. We can find the function values of y for different values of x.

x	y
-2	17
-1	7
0	1
1	-1
2	1

We can see from the table that the function y = 2x² – 4x + 1 has different values of y for different values of x. We can use these values to plot the graph of the function.

Step 3: Plotting the Points

The next step in drawing a quadratic function graph is to plot the points we found in step 2. We can use the coordinate plane to plot these points. The x-axis represents the horizontal values, and the y-axis represents the vertical values.

Let’s take the values from the table and plot them on the coordinate plane.

From the coordinate plane, we can see that the graph of the quadratic equation y = 2x² – 4x + 1 is a U-shaped curve. We can also see that the vertex of the parabola is (1,-3).

Step 4: Drawing the Parabola

The final step in drawing a quadratic function graph is to draw the parabolic curve. We can draw the parabolic curve by connecting the points plotted in step 3. It is important to draw a smooth curve that passes through these points.

Let’s draw the parabolic curve for the quadratic equation y = 2x² – 4x + 1.

From the graph, we can see that the parabolic curve passes through the two points plotted in step 3. We can also see that the vertex of the parabola is (1,-3), which we found in step 2.

FAQs

1. What is a quadratic function?

A quadratic function is a mathematical function that can be represented by a second-degree polynomial equation. The equation of the quadratic function is y = ax² + bx + c. Here, a, b and c are constants and x is a variable.

2. What is a parabola?

A parabola is a U-shaped curve that can be formed by plotting the graph of a quadratic function. The shape of the parabola is defined by the value of the coefficient a in the quadratic equation.

3. How can we find the vertex of a parabola?

The vertex of a parabola is the point where it changes its direction. The vertex lies on the axis of symmetry, which is the vertical line that passes through the vertex. We can find the vertex by using the formula x = -b/2a and substituting the value of x to the equation to find the value of y.

4. How many points do we need to draw a quadratic function graph?

To draw a quadratic function graph, we need a minimum of two points. These points can be found by substituting different values of x to the given quadratic equation.

5. How can we draw a smooth curve that passes through the points?

To draw a smooth curve that passes through the points, we can use a freehand drawing tool or a ruler. It is important to draw a smooth curve that follows the pattern of the parabolic curve.

6. What is the significance of the axis of symmetry?

The axis of symmetry is the vertical line that passes through the vertex of a parabola. The axis of symmetry divides the parabola into two equal halves. This line is significant because it helps us to find the vertex and also to understand the symmetrical properties of the parabola.

Conclusion

In conclusion, drawing the graph of a quadratic function can be a simple and straightforward process if we follow the steps mentioned above. We need to have a basic understanding of the concept and compute the function values for different values of x. We can plot the points on the coordinate plane and draw a smooth curve that passes through these points. By following these steps, we can draw the graph of any quadratic function easily.

Cara Menggambar Grafik Fungsi Kuadrat