An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
A quadratic function has the form f ( x ) = a x 2 + b x + c , where a = 0 .
Examine each function to determine its degree.
f ( x ) = − 7 x 2 − x + 2 has degree 2 and a = − 7 = 0 , so it is a quadratic function.
The quadratic function is f ( x ) = − 7 x 2 − x + 2 .
Explanation
Understanding Quadratic Functions We are given four functions and asked to identify the quadratic function. A quadratic function is a polynomial function of degree 2. The general form of a quadratic function is f ( x ) = a x 2 + b x + c , where a = 0 .
Analyzing Each Function Let's examine each function to determine its degree.
f ( x ) = − 7 x 2 − x + 2 : This function has degree 2, with a = − 7 , b = − 1 , and c = 2 . Since a = 0 , this is a quadratic function.
f ( x ) = − 3 x + 2 : This function has degree 1. It is a linear function, not a quadratic function.
f ( x ) = 0 x 2 + 3 x − 3 : This function has degree 1, since the x 2 term vanishes. It is a linear function, not a quadratic function.
f ( x ) = 2 x 3 + 2 x 2 − 4 : This function has degree 3. It is a cubic function, not a quadratic function.
Identifying the Quadratic Function The function f ( x ) = − 7 x 2 − x + 2 is the only function with degree 2 and a non-zero coefficient for the x 2 term. Therefore, it is the quadratic function.
Final Answer The quadratic function is f ( x ) = − 7 x 2 − x + 2 .
Examples
Quadratic functions are used in many real-world applications, such as modeling the trajectory of a ball, designing parabolic mirrors, and determining the optimal dimensions for a rectangular garden. Understanding quadratic functions helps in solving problems related to optimization, physics, and engineering. For example, if you want to find the maximum height a ball reaches when thrown, you can model the ball's path using a quadratic function and find its vertex, which represents the maximum height.
Approximately 2.81 × 1 0 21 electrons flow through the electric device delivering a current of 15.0 A for 30 seconds, calculated using the relationship between current, charge, and the charge of an electron.
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