Which function is a quadratic function?
[tex]f(x)=2 x^2[/tex]
[tex]g(x)=5 x^3[/tex]
[tex]k(x)=-x[/tex]
[tex]b(x)=-9 x^4[/tex]
Answer (2)
The only quadratic function among the given options is f ( x ) = 2 x 2 , which follows the form a x 2 + b x + c with a = 2 . Other functions either represent cubic or linear forms, which do not qualify as quadratic functions.
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A quadratic function has the form a x 2 + b x + c , where a e q 0 .
Examine each function to determine if it fits the quadratic form.
f ( x ) = 2 x 2 fits the form with a = 2 , b = 0 , and c = 0 .
The quadratic function is f ( x ) = 2 x 2 .
Explanation
Understanding Quadratic Functions A quadratic function is a polynomial function of degree 2. This means it can be written in the form a x 2 + b x + c , where a is not zero. We need to check each of the given functions to see if they fit this form.
Checking Each Function Let's examine each function:
f ( x ) = 2 x 2 : This function has a term with x 2 and no higher powers of x . It fits the form a x 2 + b x + c with a = 2 , b = 0 , and c = 0 .
g ( x ) = 5 x 3 : This function has a term with x 3 , which means it's a cubic function, not a quadratic function.
k ( x ) = − x : This function has a term with x to the power of 1. It's a linear function, not a quadratic function.
b ( x ) = − 9 x 4 : This function has a term with x 4 , which means it's a quartic function, not a quadratic function.
Identifying the Quadratic Function Therefore, the only quadratic function among the given options is f ( x ) = 2 x 2 .
Examples
Quadratic functions are used in many real-world applications, such as modeling the trajectory of a ball thrown in the air. The height of the ball at any given time can be described by a quadratic function. Similarly, the shape of a satellite dish or a suspension bridge cable can be modeled using quadratic functions. Understanding quadratic functions helps us predict and analyze these types of phenomena.
