1. What is a Quadratic Function?

A quadratic function is a second-degree polynomial function of the form f(x) = ax² + bx + c, where a, b, and c are constants with a ≠ 0. Its graph is a parabola that opens upward if a > 0 and downward if a < 0.

2. How to Find Maximum/Minimum?

The vertex of the parabola represents the maximum or minimum point of the quadratic function:

Where:

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

Explanation: The vertex formula is derived from completing the square or using calculus. The x-coordinate of the vertex is -b/(2a), and the y-coordinate is found by plugging this x-value back into the original equation.

3. Importance of Vertex Calculation

Details: Finding the vertex is crucial for optimization problems, projectile motion analysis, and understanding the behavior of quadratic functions in physics, engineering, and economics.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c of your quadratic function. The calculator will find the vertex coordinates and determine whether it's a maximum or minimum point.

5. Frequently Asked Questions (FAQ)

Q1: What if a = 0?
A: If a = 0, the function is linear, not quadratic, and doesn't have a maximum or minimum (unless it's a constant function).

Q2: How accurate are the results?
A: Results are accurate to 4 decimal places. For exact fractions, manual calculation may be needed.

Q3: Can this calculator find roots?
A: This calculator focuses on finding the vertex. For roots, you would need to use the quadratic formula.

Q4: What's the difference between vertex and roots?
A: The vertex is the maximum/minimum point, while roots are the x-intercepts (where f(x) = 0).

Q5: How does this relate to calculus?
A: The vertex represents the critical point where the derivative (slope) of the function is zero.