Which quadratic function in standard form has the values \(a=-3.5\), \(b=2.7\), and \(c=-8.2\)?

A. \(f(x) = 2.7 x^2 - 8.2 x - 3.5\)

B. \(f(x) = 2.7 x^2 - 3.5 x - 8.2\)

C. \(f(x) = -3.5 x^2 - 8.2 x + 2.7\)

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



Answer :

To determine which quadratic function in standard form matches the given values \( a = -3.5 \), \( b = 2.7 \), and \( c = -8.2 \), let’s recall the general structure of a quadratic function. A quadratic function in its standard form is expressed as:

[tex]\[ f(x) = ax^2 + bx + c \][/tex]

We need to identify which of the provided functions fits this form with the specific coefficients \( a \), \( b \), and \( c \).

Let's go through each option to see which one matches:

1. Option 1: \( f(x) = 2.7x^2 - 8.2x - 3.5 \)
- Here, the coefficients are:
- \( a \) (coefficient of \( x^2 \)) is \( 2.7 \)
- \( b \) (coefficient of \( x \)) is \( -8.2 \)
- \( c \) (constant term) is \( -3.5 \)
- Compare with given values:
- \( a = 2.7 \) (incorrect, should be \( -3.5 \))
- \( b = -8.2 \) (incorrect, should be \( 2.7 \))
- \( c = -3.5 \) (one correct, but overall incorrect match)

2. Option 2: \( f(x) = 2.7x^2 - 3.5x - 8.2 \)
- Here, the coefficients are:
- \( a \) is \( 2.7 \)
- \( b \) is \( -3.5 \)
- \( c \) is \( -8.2 \)
- Compare with given values:
- \( a = 2.7 \) (incorrect, should be \( -3.5 \))
- \( b = -3.5 \) (incorrect, should be \( 2.7 \))
- \( c = -8.2 \) (one correct, but overall incorrect match)

3. Option 3: \( f(x) = -3.5x^2 - 8.2x + 2.7 \)
- Here, the coefficients are:
- \( a \) is \( -3.5 \)
- \( b \) is \( -8.2 \)
- \( c \) is \( 2.7 \)
- Compare with given values:
- \( a = -3.5 \) (correct)
- \( b = -8.2 \) (incorrect, should be \( 2.7 \))
- \( c = 2.7 \) (incorrect, should be \( -8.2 \))
- Overall incorrect match

4. Option 4: \( f(x) = -3.5x^2 + 2.7x - 8.2 \)
- Here, the coefficients are:
- \( a \) is \( -3.5 \)
- \( b \) is \( 2.7 \)
- \( c \) is \( -8.2 \)
- Compare with given values:
- \( a = -3.5 \) (correct)
- \( b = 2.7 \) (correct)
- \( c = -8.2 \) (correct)
- Overall correct match

Therefore, the correct quadratic function in standard form with \( a = -3.5 \), \( b = 2.7 \), and \( c = -8.2 \) is:

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

Hence, the answer is:

[tex]\[ \boxed{4} \][/tex]