FUNGSI KUADRAT KELAS 10 KURIKULUM MERDEKA

Summary

In this lesson, the basics of quadratic functions are explored. The video covers the general form of quadratic functions, their graphical properties, and how to find the X and Y intercepts. It explains how to determine the vertex of a quadratic function and how to use factoring to solve for the roots. With clear examples and step-by-step explanations, this lesson helps students understand key concepts like the direction of the parabola, finding points of intersection with axes, and identifying maximum or minimum values of the graph. A solid foundation in quadratic functions is provided for learners.

Takeaways

• 😀 Quadratic functions are essential in understanding real-world applications like bridge cables and safety rails, which often form parabolas.
• 😀 The general form of a quadratic function is f(x) = ax² + bx + c, where 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant.
• 😀 The direction of the parabola is determined by the value of 'a': if a > 0, the parabola opens upwards; if a < 0, it opens downwards.
• 😀 To find the x-intercepts (roots) of a quadratic function, set f(x) = 0 and solve for x, often by factoring the equation.
• 😀 The y-intercept is found by substituting x = 0 into the equation and solving for f(0), showing where the graph crosses the y-axis.
• 😀 The vertex of the parabola, or the point of minimum or maximum value, is given by the formula x_vertex = -b/(2a).
• 😀 The y-coordinate of the vertex can be calculated by substituting the x-coordinate of the vertex back into the quadratic equation.
• 😀 A quadratic function's vertex represents either the maximum or minimum value, depending on whether the parabola opens upwards or downwards.
• 😀 The axis of symmetry of the parabola is the vertical line x = x_vertex, which divides the parabola into two symmetric halves.
• 😀 Example problems demonstrate how to calculate the vertex, axis of symmetry, x-intercepts, and y-intercept for a given quadratic function.

Q & A

What is a quadratic function?

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants, and a ≠ 0.

What is the general form of a quadratic function?

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants, and a cannot be 0.

What does the coefficient 'a' represent in a quadratic function?

'a' is the coefficient of x², which determines the direction of the parabola. If 'a' is positive, the parabola opens upwards, and if 'a' is negative, the parabola opens downwards.

How can you determine the direction in which a parabola opens?

You can determine the direction of the parabola by looking at the coefficient 'a'. If 'a' is positive, the parabola opens upwards; if 'a' is negative, the parabola opens downwards.

What is the method to find the x-intercepts of a quadratic function?

To find the x-intercepts (points where the graph cuts the x-axis), set f(x) = 0 and solve the quadratic equation. This can be done by factoring, completing the square, or using the quadratic formula.

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

To find the y-intercept (point where the graph cuts the y-axis), set x = 0 and calculate f(0). The result will give you the y-coordinate of the intercept.

What is the vertex of a quadratic function?

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction the parabola opens. It can be found using the formula x = -b/(2a), where a and b are the coefficients from the quadratic function.

What is the formula to find the vertex of a quadratic function?

The x-coordinate of the vertex is given by x = -b/(2a). Once you have the x-coordinate, substitute it back into the quadratic function to find the y-coordinate.

How do you calculate the discriminant of a quadratic function?

The discriminant (D) of a quadratic function is calculated using the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic function.

What does the discriminant tell you about a quadratic function?

The discriminant gives information about the number of real solutions to the quadratic equation. If D > 0, there are two real solutions; if D = 0, there is one real solution; and if D < 0, there are no real solutions.