Quadratic Function Graphing Calculator
Visualize the parabola of the equation y = ax² + bx + c
How to Use This Calculator
This tool allows you to graph quadratic functions in the standard form y = ax² + bx + c. Simply enter the numerical values for coefficients a, b, and c. You can also define the viewing window by setting the minimum and maximum values for the X-axis. Click "Plot Graph" to render the curve.
Understanding the Parameters
Coefficient a: Determines the width and direction of the parabola. If a is positive, the parabola opens upwards; if negative, it opens downwards. Larger absolute values of a make the parabola narrower.
Coefficient b: Influences the position of the vertex along the x-axis and the axis of symmetry.
Constant c: Represents the y-intercept, which is the point where the graph crosses the y-axis.
The Vertex Formula
The vertex is the highest or lowest point of the parabola. You can find the x-coordinate of the vertex using the formula:
x = -b / (2a)
Once you have x, substitute it back into the equation to find the y-coordinate. The calculator automatically calculates this point for you and displays it below the graph.