Answer
$A$
Work Step by Step
In a quadratic function, $a$ is the coefficient of the first term, $b$ is the coefficient of the second term, and $c$ is the constant term. The quadratic function has the form $y = ax^2 + bx + c$.
Let's check each of the answer options to see which one has $-3$ as the constant.
For answer option $A$, we have to use the FOIL method to rewrite the function in quadratic form. We need to multiply the first terms, then the outer, then the inner, and, finally, the last terms:
$y = (3x)(-x) + (3x)(-3) + (1)(-x) + (1)(-3)$
Multiply to simplify:
$y = -3x^2 - 9x - x - 3$
Combine like terms:
$y = -3x^2 - 10x - 3$
This answer option is correct because the constant term is $-3$.
For answer option $B$, we have to use the FOIL method to rewrite the function in quadratic form. We need to multiply the first terms, then the outer, then the inner, and, finally, the last terms:
$y = (x)(x) + (x)(-3) + (-3)(x) + (-3)(-3)$
Multiply to simplify:
$y = x^2 - 3x - 3x + 9$
Combine like terms:
$y = x^2 - 6x + 9$
This answer option is incorrect because the constant term is $9$.
For answer option $C$, the function is already in quadratic form, so if we look at the function, we see that the constant term is $3$ and not $-3$; therefore, this answer option is incorrect.
For answer option $D$, the function is already in quadratic form, so if we look at the function, we see that the constant term is $9$ and not $-3$; therefore, this answer option is incorrect.
