$f(x)=x^2-4 x^2-7 x+10$
Answer (2)
To simplify f ( x ) = x 2 − 4 x 2 − 7 x + 10 , we combine like terms to get f ( x ) = − 3 x 2 − 7 x + 10 . This represents a quadratic function that can be used in various mathematical contexts. The final simplified expression is f ( x ) = − 3 x 2 − 7 x + 10 .
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Combine the x 2 terms: x 2 − 4 x 2 = − 3 x 2 .
Rewrite the function with the combined term: f ( x ) = − 3 x 2 − 7 x + 10 .
The simplified function is f ( x ) = − 3 x 2 − 7 x + 10 .
Explanation
Understanding the Function We are given the function f ( x ) = x 2 − 4 x 2 − 7 x + 10 . Our goal is to simplify this expression by combining like terms.
Combining Like Terms We observe that the terms x 2 and − 4 x 2 are like terms, meaning they have the same variable raised to the same power. We can combine these terms by adding their coefficients: 1 x 2 − 4 x 2 = ( 1 − 4 ) x 2 = − 3 x 2 .
Simplified Function Now, we substitute this back into the original expression: f ( x ) = − 3 x 2 − 7 x + 10 . This is the simplified form of the function.
Final Answer Therefore, the simplified function is f ( x ) = − 3 x 2 − 7 x + 10 .
Examples
In physics, this type of function could describe the height of a projectile over time, where the x represents time. Simplifying the function makes it easier to analyze the projectile's trajectory, find its maximum height, and determine when it will hit the ground. For example, if f ( x ) represents the height, we can find the time at which the projectile hits the ground by solving f ( x ) = 0 .
