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Answer :
To determine which quadratic function in standard form matches the given values [tex]\(a = -3.5\)[/tex], [tex]\(b = 2.7\)[/tex], and [tex]\(c = -8.2\)[/tex], we need to construct the quadratic equation using the standard form, which is:
[tex]\[ f(x) = ax^2 + bx + c \][/tex]
Substituting the given values for [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex], we have:
[tex]\[ f(x) = -3.5x^2 + 2.7x - 8.2 \][/tex]
Now, let's compare this function to the choices provided:
1. [tex]\( f(x) = 27x^2 - 82x - 35 \)[/tex]
2. [tex]\( f(x) = 27x^2 - 35x - 8.2 \)[/tex]
3. [tex]\( f(x) = -3.5x^2 - 8.2x + 27 \)[/tex]
4. [tex]\( f(x) = -3.5x^2 + 2.7x - 8.2 \)[/tex]
We need to check which of these options has the coefficients that match what we constructed:
- For option 1, the coefficients are 27, -82, and -35. This does not match.
- For option 2, the coefficients are 27, -35, and -8.2. This does not match.
- For option 3, the coefficients are -3.5, -8.2, and 27. This does not match.
- For option 4, the coefficients are -3.5, 2.7, and -8.2. This matches perfectly.
Therefore, the quadratic function in standard form that corresponds to the given values is:
[tex]\[ f(x) = -3.5x^2 + 2.7x - 8.2 \][/tex]
This matches option 4.
[tex]\[ f(x) = ax^2 + bx + c \][/tex]
Substituting the given values for [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex], we have:
[tex]\[ f(x) = -3.5x^2 + 2.7x - 8.2 \][/tex]
Now, let's compare this function to the choices provided:
1. [tex]\( f(x) = 27x^2 - 82x - 35 \)[/tex]
2. [tex]\( f(x) = 27x^2 - 35x - 8.2 \)[/tex]
3. [tex]\( f(x) = -3.5x^2 - 8.2x + 27 \)[/tex]
4. [tex]\( f(x) = -3.5x^2 + 2.7x - 8.2 \)[/tex]
We need to check which of these options has the coefficients that match what we constructed:
- For option 1, the coefficients are 27, -82, and -35. This does not match.
- For option 2, the coefficients are 27, -35, and -8.2. This does not match.
- For option 3, the coefficients are -3.5, -8.2, and 27. This does not match.
- For option 4, the coefficients are -3.5, 2.7, and -8.2. This matches perfectly.
Therefore, the quadratic function in standard form that corresponds to the given values is:
[tex]\[ f(x) = -3.5x^2 + 2.7x - 8.2 \][/tex]
This matches option 4.
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