1. What is the Vertex of a Parabola?

The vertex of a parabola is the point where the parabola changes direction. For a quadratic function in the form y = ax² + bx + c, the vertex represents either the maximum or minimum point of the parabola.

2. How Does the Calculator Work?

The calculator uses the vertex formula:

Where:

• \( a \) — Coefficient of x² term
• \( b \) — Coefficient of x term
• \( c \) — Constant term

Explanation: The x-coordinate of the vertex is found using -b/2a, and the y-coordinate is calculated by substituting the x-value back into the original equation.

3. Importance of Vertex Calculation

Details: Finding the vertex is essential for graphing quadratic functions, solving optimization problems, and analyzing projectile motion in physics.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation in the form y = ax² + bx + c. The coefficient a must not be zero.

5. Frequently Asked Questions (FAQ)

Q1: What if my 'a' coefficient is zero?
A: If a = 0, the equation is linear, not quadratic, and doesn't have a vertex in the parabolic sense.

Q2: How do I know if the vertex is a maximum or minimum?
A: If a > 0, the parabola opens upward and the vertex is a minimum. If a < 0, it opens downward and the vertex is a maximum.

Q3: Can I use this for vertex form equations?
A: For equations already in vertex form y = a(x-h)² + k, the vertex is simply (h, k).

Q4: What's the relationship between vertex and axis of symmetry?
A: The vertical line x = -b/2a is the axis of symmetry, passing through the vertex.

Q5: How precise are the calculator's results?
A: Results are rounded to 4 decimal places, but calculations use full precision internally.