¿Cómo GRAFICAR una función CUADRÁTICA? RAÍCES, VÉRTICE, ORDENADA AL ORIGEN y MÁS

Summary

In this tutorial, Adrián and Christina explain how to graph a quadratic function, specifically the equation y = x² + 6x + 5. They walk through determining the values of a, b, and c, using the quadratic formula to find the roots of the parabola. They then calculate the vertex and the axis of symmetry, showing how to plot the function on a Cartesian plane. The video also highlights the direction of the parabola based on the value of a. Viewers are encouraged to explore more quadratic function content from their channel.

Takeaways

• 😀 The video tutorial explains how to graph a quadratic function.
• 😀 The equation given is f(x) = x² + 6x + 5, which is a quadratic function.
• 😀 The coefficients a, b, and c are identified in the quadratic equation: a = 1, b = 6, c = 5.
• 😀 To find the roots (x-intercepts), the quadratic formula is used: x = (-b ± √(b² - 4ac)) / 2a.
• 😀 The discriminant is calculated as 36 - 20 = 16, and its square root gives 4.
• 😀 The two roots of the equation are x₁ = -1 and x₂ = -5, which are plotted on the Cartesian plane.
• 😀 The vertex of the parabola is located at x = -3 by averaging the two roots.
• 😀 The y-coordinate of the vertex is found by substituting x = -3 into the original equation, yielding y = -4.
• 😀 The axis of symmetry is a vertical line at x = -3, which divides the parabola into two equal halves.
• 😀 The parabola intersects the y-axis at the point (0, 5), as given by the value of c.
• 😀 The graph of the parabola is drawn by connecting the identified points and reflecting symmetry around the axis of symmetry.
• 😀 The parabola opens upwards because the coefficient a is positive (a = 1).

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