What is the value of [tex]f(x)=3 x^2+4[/tex] when [tex]x=-3[/tex]?
Answer (2)
To find f ( − 3 ) for the function f ( x ) = 3 x 2 + 4 , we substitute − 3 for x . After calculating, we find that f ( − 3 ) = 31 .
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Substitute x = − 3 into the function f ( x ) = 3 x 2 + 4 .
Calculate ( − 3 ) 2 = 9 .
Multiply 3 × 9 = 27 .
Add 27 + 4 = 31 . The final answer is 31 .
Explanation
Understanding the problem We are given the function f ( x ) = 3 x 2 + 4 and we want to find the value of the function when x = − 3 . This means we need to substitute − 3 for x in the expression for f ( x ) .
Substitution Now, we substitute x = − 3 into the function: f ( − 3 ) = 3 ( − 3 ) 2 + 4
Squaring -3 Next, we simplify the expression. First, we calculate ( − 3 ) 2 which is ( − 3 ) × ( − 3 ) = 9 . So we have: f ( − 3 ) = 3 ( 9 ) + 4
Multiplication Then, we multiply 3 by 9 , which gives us 27 . So we have: f ( − 3 ) = 27 + 4
Addition Finally, we add 27 and 4 , which gives us 31 . Therefore, the value of the function f ( x ) when x = − 3 is 31 .
f ( − 3 ) = 31
Final Answer Thus, the value of f ( x ) = 3 x 2 + 4 when x = − 3 is 31 .
Examples
Imagine you are designing a parabolic mirror for a telescope. The function f ( x ) = 3 x 2 + 4 describes the shape of the mirror. If you want to know the height of the mirror at a point 3 units away from the center (x = -3), you would calculate f(-3) to find that height. This type of calculation is crucial in optics and engineering to ensure that the mirror focuses light correctly.
