Parabola Equation Calculator

Using the Parabola Equation Calculator

The Parabola Equation Calculator is a tool designed to determine various properties of a quadratic function of the form ax² + bx + c = 0. Follow the guide below to use the calculator effectively.

Input Section

1. a (coefficient of x²):
   • Enter the value of a in the provided input field. This value represents the coefficient of x².
   • Ensure the field is not left empty, as it is a required field.
2. b (coefficient of x):
   • Enter the value of b. This value is the coefficient of x.
   • Ensure the field is not left empty, as it is a required field.
3. c (constant term):
   • Input the constant value c in this field.
   • Ensure the field is not left empty, as it is a required field.

Result Section

Once you enter the required values, the calculator will compute and display the following results:

• Vertex (x): This value is calculated using the formula -b / (2a) and gives the x-coordinate of the vertex of the parabola.
• Vertex (y): Calculated using the formula -b² / (4a) + c, it gives the y-coordinate of the vertex.
• Axis of Symmetry: Shown as x = -b / (2a), this is a vertical line that goes through the vertex, and the parabola is symmetric about this line.
• Discriminant: Using the formula b² – 4ac, this value helps determine the nature of the roots.
• First Root and Second Root: These are calculated using the quadratic formula and give the x-intercepts of the parabola, if they exist.
• Opening Direction: This shows whether the parabola opens upward or downward based on the value of a. If a is positive, the opening direction is upward; if negative, it’s downward.

Utilizing this step-by-step approach ensures you input the required data accurately and interpret the outputs effectively to understand the characteristics of the quadratic equation you are analyzing.