which graph represents y 1 2 x 2

Guri Bee

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18-10-2024

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Unveiling the Graph of y = 1 + 2x²: A Guide to Quadratic Equations

The equation y = 1 + 2x² represents a quadratic function, which is characterized by its distinctive parabolic shape. This article will guide you through the process of identifying the correct graph for this equation, building your understanding of quadratic functions along the way.

Understanding the Equation

Let's break down the equation y = 1 + 2x²:

• Constant term (1): This term dictates the vertical shift of the parabola. Since it's positive, the parabola will be shifted upwards by one unit.
• Coefficient of x² (2): This coefficient determines the "steepness" or "narrowness" of the parabola. A larger coefficient results in a narrower parabola.
• x²: The squared term indicates the parabolic shape.

Finding the Correct Graph

To find the correct graph, we'll consider the following key features:

• Vertex: The lowest point (or highest point if the coefficient of x² is negative) of the parabola.
• Symmetry: The parabola is symmetrical around a vertical line passing through the vertex.
• Direction: The parabola opens upwards since the coefficient of x² is positive.

Let's Visualize it

Imagine a graph with the x and y axes. Due to the constant term of 1, the parabola will be shifted one unit upwards. Now, consider the coefficient of x² being 2. This means the parabola will be narrower than a standard parabola (y = x²).

Identifying the Graph

To pinpoint the correct graph, look for one that:

• Opens upwards.
• Has its vertex at (0, 1) due to the vertical shift.
• Is narrower than a standard parabola.

Additional Notes

• You can always plot a few points to confirm your findings. For example, substitute x = -1, 0, and 1 into the equation to find the corresponding y values and plot them on the graph.
• The graph of a quadratic function always intersects the y-axis at the point where x = 0. In this case, substituting x = 0 into the equation yields y = 1, confirming the y-intercept.

In Conclusion

Understanding the relationship between the equation and its graph is crucial in visualizing quadratic functions. By analyzing the key features of the equation y = 1 + 2x², we can accurately identify its graph as a parabola that opens upwards, has its vertex at (0, 1), and is narrower than a standard parabola.