Challenge: Visualize Quadratic Functions
Quadratic functions are a fundamental concept in mathematics, typically written in the form y = ax^2 + bx + c, where a, b, and c are real-number coefficients. The graph of a quadratic function is a curve called a parabola. The coefficient a determines whether the parabola opens upwards (a > 0) or downwards (a < 0), while b and c affect the position and orientation of the curve. Visualizing quadratic functions helps you understand their behavior, such as their vertex, axis of symmetry, and intercepts. Plotting these functions on a graph provides valuable insight into how changing the coefficients influences the shape and position of the parabola.
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Write a function that plots the graph of a quadratic function y = ax^2 + bx + c for a range of x values. The function should take three parameters: a, b, and c, representing the coefficients of the quadratic function.
- Create an array of x values covering a suitable range.
- Compute the corresponding y values for the quadratic function using the given coefficients.
- Plot the resulting curve using
matplotlib. - Label the x and y axes.
- Add a title to the plot that includes the values of
a,b, andc. - Ensure the plot has a visible grid.
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Quadratic functions are a fundamental concept in mathematics, typically written in the form y = ax^2 + bx + c, where a, b, and c are real-number coefficients. The graph of a quadratic function is a curve called a parabola. The coefficient a determines whether the parabola opens upwards (a > 0) or downwards (a < 0), while b and c affect the position and orientation of the curve. Visualizing quadratic functions helps you understand their behavior, such as their vertex, axis of symmetry, and intercepts. Plotting these functions on a graph provides valuable insight into how changing the coefficients influences the shape and position of the parabola.
Swipe to start coding
Write a function that plots the graph of a quadratic function y = ax^2 + bx + c for a range of x values. The function should take three parameters: a, b, and c, representing the coefficients of the quadratic function.
- Create an array of x values covering a suitable range.
- Compute the corresponding y values for the quadratic function using the given coefficients.
- Plot the resulting curve using
matplotlib. - Label the x and y axes.
- Add a title to the plot that includes the values of
a,b, andc. - Ensure the plot has a visible grid.
Рішення
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