Parabola Graph Calculator

How to Use the Parabola Graph Calculator

This step-by-step guide will help you effectively use the Parabola Graph Calculator to determine various key elements of a quadratic function in the form of ax² + bx + c. Follow the instructions below to input your values and interpret the results.

Step 1: Enter Input Values

1. a (coefficient of x²): Locate the input field labeled ‘a (coefficient of x²)’. Enter the coefficient of the x² term from your quadratic equation. This value must be a number and cannot be omitted.
2. b (coefficient of x): Next, in the input field labeled ‘b (coefficient of x)’, enter the coefficient for the x term. This is also required and must be numeric.
3. c (constant term): Enter the constant term of your quadratic equation in the field labeled ‘c (constant term)’. It should be a numeric value as well.
4. x (input value): Finally, enter the x-value for which you want to compute the y-value of the parabola. This value is required for generating specific points on the parabola graph.

All input fields accept numeric values with a precision of up to one decimal. Make sure each input is completed as they are required for the calculations.

Step 2: Understand the Result Fields

After entering the input values, the calculator will compute and display the results in the Result Fields. Here’s how to interpret each one:

1. Y Value: This is the value of the quadratic function at the entered x, calculated using the formula a*x² + b*x + c. It is displayed up to two decimal places.
2. Vertex X: Shows the x-coordinate of the vertex of the parabola, calculated as -b / (2 * a).
3. Vertex Y: This indicates the y-coordinate of the vertex, calculated using the formula c – (b² / (4 * a)). Together with Vertex X, it provides the vertex point.
4. Axis of Symmetry: Displays the equation of the line of symmetry for the parabola, which is x = -b / (2 * a).
5. Discriminant: Computes the discriminant value of the equation: b² – 4ac. This helps determine the nature of the roots (real or complex).
6. Root 1 and Root 2: These fields show the roots of the quadratic equation solved using the quadratic formula. If the roots are real, they will be displayed up to two decimal points.

Each of these outputs provides insight into different characteristics of the quadratic function, helping you analyze its graph and properties.

Conclusion

By following these steps, you can use the Parabola Graph Calculator to effectively evaluate and analyze the characteristics of a quadratic function. It aids in understanding the behavior of parabolas through computed details like vertex, axis of symmetry, discriminant, and roots. Ensure all inputs are filled correctly for accurate results.