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Which is a quadratic function having a leading coefficient of 3 and a constant term of -12?

A. [tex]f(x)=-12x^2 + 3x + 1[/tex]
B. [tex]f(x)=3x^2 + 11x - 12[/tex]
C. [tex]f(x)=12x^2 + 3x + 3[/tex]
D. [tex]f(x)=3x - 12[/tex]

Sagot :

GinnyAnsweridn
To determine which quadratic function has a leading coefficient of 3 and a constant term of -12, we need to:

1. Identify the leading coefficient of each quadratic function.
2. Identify the constant term of each quadratic function.
3. Check which function satisfies both conditions: having a leading coefficient of 3 and a constant term of -12.

Let's analyze each given function:

- For [tex]\( f(x) = -12x^2 + 3x + 1 \)[/tex]:
- The leading coefficient is -12.
- The constant term is 1.
- This does not meet the criteria.

- For [tex]\( f(x) = 3x^2 + 11x - 12 \)[/tex]:
- The leading coefficient is 3.
- The constant term is -12.
- This meets the criteria.

- For [tex]\( f(x) = 12x^2 + 3x + 3 \)[/tex]:
- The leading coefficient is 12.
- The constant term is 3.
- This does not meet the criteria.

- For [tex]\( f(x) = 3x - 12 \)[/tex]:
- This is not a quadratic function; it is a linear function.
- Hence, it does not meet the criteria.

After evaluating all the given options, the quadratic function that has a leading coefficient of 3 and a constant term of -12 is:
[tex]\[ f(x) = 3x^2 + 11x - 12 \][/tex]

Thus, the correct answer is:
[tex]\[ f(x) = 3x^2 + 11x - 12 \][/tex]
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