1. What is a Vertex Calculator for Parabolas?

Definition: This calculator finds the vertex (h, k) of a parabola given its quadratic equation coefficients.

Purpose: It helps students and professionals quickly determine the vertex of a parabola without manual calculations.

2. How Does the Calculator Work?

The calculator uses the vertex formula:

Where:

• \( h \) — x-coordinate of the vertex
• \( k \) — y-coordinate of the vertex
• \( a, b, c \) — Coefficients from the quadratic equation \( f(x) = ax^2 + bx + c \)

Explanation: The x-coordinate (h) is found using -b/2a, then k is calculated by plugging h back into the original equation.

3. Importance of Vertex Calculation

Details: The vertex represents either the maximum or minimum point of a parabola, crucial for graphing and solving optimization problems.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. Coefficient a cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What if my 'a' coefficient is zero?
A: The equation wouldn't be quadratic (no parabola). The calculator requires a ≠ 0.

Q2: How accurate are the results?
A: Results are accurate to 3 decimal places, sufficient for most applications.

Q3: Does this work for vertical parabolas?
A: This calculator handles standard quadratic functions (y = ax² + bx + c). For x = ay² + by + c, use different methods.

Q4: What does the vertex represent?
A: For a > 0, it's the minimum point. For a < 0, it's the maximum point of the parabola.

Q5: Can I use fractions or decimals?
A: Yes, the calculator accepts both fractional and decimal inputs.