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When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown?

[tex]\[2 + 7c - 4c^2 - 3c + 4\][/tex]

A. \(-4c^2 + 4c + 6\)

B. \(-7c^2 + 10c + 6\)

C. \(-4c^2 + 4c + 8\)

D. [tex]\(-7c^2 + 7c + 6\)[/tex]

Sagot :

GinnyAnswer
To simplify the given polynomial \(2 + 7c - 4c^2 - 3c + 4\) and write it in standard form, follow these steps:

1. Identify and combine like terms:
- Constant terms: \(2\) and \(4\)
- Linear terms (terms with \(c\)): \(7c\) and \(-3c\)
- Quadratic term (term with \(c^2\)): \(-4c^2\)

2. Combine the constant terms:
[tex]\[ 2 + 4 = 6 \][/tex]

3. Combine the linear terms:
[tex]\[ 7c - 3c = 4c \][/tex]

4. Write down the quadratic term:
[tex]\[ -4c^2 \][/tex]

5. Put all the simplified terms together to write the polynomial in standard form:
[tex]\[ -4c^2 + 4c + 6 \][/tex]

Now, we need to match this simplified polynomial to one of the given options.

The given options are:
1. \(-4c^2 + 4c + 6\)
2. \(-7c^2 + 10c + 6\)
3. \(-4c^2 + 4c + 8\)
4. \(-7c^2 + 7c + 6\)

From the options, the polynomial \(-4c^2 + 4c + 6\) exactly matches the simplified form of the given polynomial.

Therefore, the quadratic function that is equivalent to the given polynomial is:
[tex]\[ \boxed{-4c^2 + 4c + 6} \][/tex]
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