Which Represents A Quadratic Function?A. F ( X ) = 2 X 3 + 2 X 2 − 4 F(x) = 2x^3 + 2x^2 - 4 F ( X ) = 2 X 3 + 2 X 2 − 4 B. F ( X ) = − 7 X 2 − X + 2 F(x) = -7x^2 - X + 2 F ( X ) = − 7 X 2 − X + 2 C. F ( X ) = − 3 X + 2 F(x) = -3x + 2 F ( X ) = − 3 X + 2 D. F ( X ) = 0 X 2 + 3 X − 3 F(x) = 0x^2 + 3x - 3 F ( X ) = 0 X 2 + 3 X − 3

**Which Represents a Quadratic Function?** =====================================================

A quadratic function is a polynomial function of degree two, which means the highest power of the variable (in this case, x) is two. It has the general form of f(x) = ax^2 + bx + c, where a, b, and c are constants, and a cannot be equal to zero.

In this article, we will examine four different functions and determine which one represents a quadratic function.

What is a Quadratic Function?

A quadratic function is a polynomial function of degree two, which means the highest power of the variable (in this case, x) is two. It has the general form of f(x) = ax^2 + bx + c, where a, b, and c are constants, and a cannot be equal to zero.

Quadratic functions can be written in the form of f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. This form is called the vertex form of a quadratic function.

Which of the Following Functions Represents a Quadratic Function?

Let's examine the four functions given in the problem:

A. $f(x) = 2x^3 + 2x^2 - 4$ B. $f(x) = -7x^2 - x + 2$ C. $f(x) = -3x + 2$ D. $f(x) = 0x^2 + 3x - 3$

To determine which function represents a quadratic function, we need to examine the highest power of the variable (x) in each function.

Function A: $f(x) = 2x^3 + 2x^2 - 4$

The highest power of the variable (x) in this function is three, which means it is a cubic function, not a quadratic function.

Function B: $f(x) = -7x^2 - x + 2$

The highest power of the variable (x) in this function is two, which means it is a quadratic function.

Function C: $f(x) = -3x + 2$

The highest power of the variable (x) in this function is one, which means it is a linear function, not a quadratic function.

Function D: $f(x) = 0x^2 + 3x - 3$

The highest power of the variable (x) in this function is one, which means it is a linear function, not a quadratic function.

Conclusion

Based on the examination of the four functions, we can conclude that only one function represents a quadratic function.

Answer

The correct answer is B. $f(x) = -7x^2 - x + 2$.

Frequently Asked Questions

Q: What is a quadratic function?

A: A quadratic function is a polynomial function of degree two, which means the highest power of the variable (in this case, x) is two. It has the general form of f(x) = ax^2 + bx + c, where a, b, and c are constants, and a cannot be equal to zero.

Q: What is the vertex form of a quadratic function?

A: The vertex form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Q: How do I determine if a function is quadratic or not?

A: To determine if a function is quadratic or not, you need to examine the highest power of the variable (x) in the function. If the highest power is two, then the function is quadratic. If the highest power is one or three, then the function is linear or cubic, respectively.

Q: What is the difference between a quadratic function and a linear function?

A: The main difference between a quadratic function and a linear function is the highest power of the variable (x). A quadratic function has a highest power of two, while a linear function has a highest power of one.

Q: What is the difference between a quadratic function and a cubic function?

A: The main difference between a quadratic function and a cubic function is the highest power of the variable (x). A quadratic function has a highest power of two, while a cubic function has a highest power of three.