1. What Is The X2 6x Function?

The function f(x) = x² + 6x is a quadratic function that represents a parabola opening upwards. It is commonly used in mathematics to model various real-world phenomena and solve optimization problems.

2. How Does The Calculator Work?

The calculator uses the quadratic function formula:

Where:

• \( x \) — Input value for the function
• \( x^2 \) — Square of the input value
• \( 6x \) — Six times the input value

Explanation: The calculator computes the sum of the squared input value and six times the input value to determine the function output.

3. Applications Of Quadratic Functions

Details: Quadratic functions like f(x) = x² + 6x are used in physics for projectile motion, in economics for cost and revenue functions, and in engineering for various optimization problems.

4. Using The Calculator

Tips: Enter any real number value for x. The calculator will compute and display the corresponding function value f(x) = x² + 6x.

5. Frequently Asked Questions (FAQ)

Q1: What type of function is f(x) = x² + 6x?
A: This is a quadratic function, specifically a second-degree polynomial function.

Q2: What is the vertex of this parabola?
A: The vertex of f(x) = x² + 6x is at x = -3, with a function value of -9.

Q3: What are the roots of this function?
A: The roots are x = 0 and x = -6, where the function equals zero.

Q4: Can this function model real-world scenarios?
A: Yes, quadratic functions are commonly used to model projectile motion, area problems, and various optimization scenarios.

Q5: How does this function behave for large values of x?
A: As x approaches positive or negative infinity, the x² term dominates, causing the function to approach positive infinity.