To determine the required quadratic function in standard form, let us match the given coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] in the general expression of a quadratic function which is:
[tex]\[ f(x) = ax^2 + bx + c \][/tex]
Given the values:
- [tex]\(a = -3.5\)[/tex]
- [tex]\(b = 2.7\)[/tex]
- [tex]\(c = -8.2\)[/tex]
The quadratic function should include the terms with the correct coefficients for [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and the constant. Substituting the given values into the quadratic form, we get:
[tex]\[ f(x) = -3.5x^2 + 2.7x -8.2 \][/tex]
Now, we need to find this expression among the given choices:
1. [tex]\( f(x) = 2.7x^2 - 8.2x - 3.5 \)[/tex]
2. [tex]\( f(x) = 2.7x^2 - 3.5x - 8.2 \)[/tex]
3. [tex]\( f(x) = -3.5x^2 - 8.2x + 2.7 \)[/tex]
4. [tex]\( f(x) = -3.5x^2 + 2.7x - 8.2 \)[/tex]
Clearly, the expression [tex]\( f(x) = -3.5x^2 + 2.7x - 8.2 \)[/tex] matches the given coefficients [tex]\(a = -3.5\)[/tex], [tex]\(b = 2.7\)[/tex], and [tex]\(c = -8.2\)[/tex].
Thus, the correct quadratic function is:
[tex]\[ \boxed{f(x) = -3.5x^2 + 2.7x - 8.2} \][/tex]
And this corresponds to option 4.
