4 PASSOS PARA CONSTRUIR UMA PARÁBOLA | GRÁFICO DO 2º GRAU

Summary

In this video, the instructor explains how to quickly construct a graph of a quadratic function. The process includes determining whether the parabola opens upwards or downwards, finding the roots using the quadratic formula (Bhaskara's method), and plotting the graph. The instructor emphasizes the importance of the vertex, explaining how to find the x and y coordinates using formulas. With clear steps, the instructor guides viewers through understanding the function's graph, roots, and vertex, ultimately helping viewers grasp key concepts of quadratic functions in a practical and engaging way.

Takeaways

• 😀 Understand whether the parabola opens upwards or downwards based on the coefficient 'a' in the quadratic equation.
• 😀 To find the roots of the parabola, you can use methods like sum and product or the quadratic formula (Bhaskara).
• 😀 The discriminant (Δ) is used to determine the nature of the roots. If Δ > 0, there are two distinct roots.
• 😀 The roots of the quadratic function are the points where the parabola intersects the x-axis.
• 😀 The parabola always intersects the y-axis at the value of the constant term 'c' (the y-intercept).
• 😀 The vertex of the parabola is the point where the curve changes direction, and it's always equidistant from the two roots.
• 😀 To calculate the x-coordinate of the vertex, use the formula x = -b / 2a.
• 😀 The y-coordinate of the vertex can be calculated using the formula y = -Δ / 4a, where Δ is the discriminant.
• 😀 The vertex represents the minimum or maximum point of the parabola, depending on whether it opens upwards or downwards.
• 😀 By knowing the x-coordinate of the vertex, you can easily substitute it into the quadratic equation to find the corresponding y-coordinate.

Q & A

What is the first step in graphing a quadratic function?

The first step is to determine if the parabola opens upwards or downwards by looking at the leading coefficient 'a' of the quadratic function. If 'a' is positive, the parabola opens upwards, and if 'a' is negative, the parabola opens downwards.

How do you find the roots of a quadratic function?

To find the roots, you can use the quadratic formula or factorization methods. In the script, the method used is Bhaskara's formula, which involves calculating the discriminant (Δ) and then applying the formula: x = (-b ± √Δ) / 2a.

What does the discriminant (Δ) tell you about the roots of a quadratic function?

The discriminant (Δ) helps determine the nature of the roots. If Δ > 0, there are two real roots. If Δ = 0, there is one real root (the vertex touches the x-axis). If Δ < 0, there are no real roots.

Why are the roots important when graphing a quadratic function?

The roots are important because they indicate where the parabola crosses the x-axis. These points are key in determining the overall shape and position of the graph.

How do you find the vertex of a parabola?

The x-coordinate of the vertex can be found using the formula x = -b / 2a. Once the x-coordinate is known, substitute it back into the original equation to find the y-coordinate of the vertex.

What is the significance of the vertex in a quadratic function?

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards. It represents the maximum or minimum value of the quadratic function.

How can you find the y-intercept of a quadratic function?

The y-intercept is found by setting x = 0 in the quadratic equation. This will give the value of y, which corresponds to the constant term 'c' in the quadratic function.

Why is the value of the constant term 'c' important in graphing a quadratic function?

The constant term 'c' is crucial because it determines where the parabola intersects the y-axis. The y-intercept always occurs at y = c, so it provides a key reference point for graphing.

What does it mean for a quadratic function to 'smile' or 'frown'?

A quadratic function 'smiles' if the parabola opens upwards, which happens when the leading coefficient 'a' is positive. It 'frowns' if the parabola opens downwards, which occurs when 'a' is negative.

How do you graph the quadratic function once you have the roots, vertex, and y-intercept?

After plotting the roots on the x-axis, the vertex, and the y-intercept on the graph, you can sketch the curve of the parabola. The curve should pass smoothly through these points, forming the shape of the parabola.