College

Which quadratic function in standard form has the values [tex] a = -3.5, b = 2.7, [/tex] and [tex] c = -8.2 [/tex]?

A. [tex] f(x) = 27x^2 - 82x - 35 [/tex]

B. [tex] f(x) = 27x^2 - 35x - 8.2 [/tex]

C. [tex] f(x) = -3.5x^2 - 8.2x + 27 [/tex]

D. [tex] f(x) = -3.5x^2 + 2.7x - 8.2 [/tex]

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.