which graph matches the equation y 3 2 x 3

Lyra Rowan

2 min read

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29-09-2024

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Unlocking the Secrets of Graphs: Visualizing y = 3x^2 + 2x + 3

Have you ever stared at a mathematical equation and wished you could see what it looked like? That's where graphs come in! They provide a visual representation of equations, making it easier to understand their relationships and behavior.

Let's dive into the world of graphs and explore the equation y = 3x^2 + 2x + 3. We'll use the insights from Brainly, a popular online learning platform, to help us understand the relationship between the equation and its corresponding graph.

Brainly Question: Which graph matches the equation y = 3x^2 + 2x + 3?

Brainly Answer (by user 'TheMathWiz'): The graph of this equation is a parabola. It opens upwards because the coefficient of x^2 is positive (3). To find the vertex, we can use the formula x = -b/2a, where a = 3 and b = 2. This gives us x = -2/6 = -1/3. Substituting this value of x back into the equation gives us y = 3(-1/3)^2 + 2(-1/3) + 3 = 8/3. So, the vertex of the parabola is at (-1/3, 8/3).

Analysis:

• Parabola: The Brainly answer correctly identifies the graph as a parabola. The equation y = 3x^2 + 2x + 3 is a quadratic equation, and quadratic equations always graph as parabolas.
• Vertex: The vertex is the highest or lowest point of a parabola. The formula x = -b/2a provided by 'TheMathWiz' is used to find the x-coordinate of the vertex.
• Direction: The coefficient of the x^2 term determines the direction of the parabola. A positive coefficient (like our 3) indicates the parabola opens upwards. A negative coefficient would make it open downwards.

Adding Value:

• Practical Applications: Parabolas have real-world applications in areas like physics (projectile motion) and architecture (archways). Understanding the graph of this equation could help you analyze these real-world situations.
• Graphing Software: You can use graphing software like Desmos or GeoGebra to visualize the graph of y = 3x^2 + 2x + 3. This allows you to explore how the equation behaves with different values of x, helping you confirm the insights we discussed.

Let's summarize: The graph of y = 3x^2 + 2x + 3 is a parabola opening upwards. Its vertex is located at (-1/3, 8/3). By understanding the relationship between equations and graphs, you gain a deeper understanding of how mathematical concepts are applied in the real world. Remember, visualization is key!