1. What is a Parabola?

A parabola is a U-shaped curve that can be represented by a quadratic equation of the form y = ax² + bx + c. It's a fundamental concept in algebra and appears in many real-world applications.

2. How Does the Calculator Work?

The calculator uses the quadratic equation:

Where:

• \( a \) — Determines the parabola's width and direction
• \( b \) — Affects the position of the vertex
• \( c \) — The y-intercept point

Explanation: The calculator computes key features including the vertex, roots, y-intercept, and discriminant to fully describe the parabola.

3. Importance of Parabola Calculations

Details: Understanding parabolas is essential in physics (projectile motion), engineering (structural design), economics (profit curves), and many other fields.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. Coefficient a cannot be zero (that would make it a linear equation).

5. Frequently Asked Questions (FAQ)

Q1: What if the discriminant is negative?
A: A negative discriminant means the parabola doesn't intersect the x-axis (no real roots).

Q2: What does the vertex represent?
A: The vertex is either the highest or lowest point on the parabola, depending on its direction.

Q3: How does coefficient 'a' affect the parabola?
A: If a > 0, parabola opens upwards; if a < 0, it opens downwards. Larger absolute values of a make the parabola narrower.

Q4: What's the significance of the discriminant?
A: The discriminant (b² - 4ac) determines the nature and number of roots the equation has.

Q5: Can I use this for vertex form equations?
A: First convert vertex form (y = a(x-h)² + k) to standard form by expanding the squared term.