Building an Algebraic Expression Using Values a = -1, b = -6, c = 9

To solve this problem, we need to create a quadratic expression using the given parameters.

Step 1: Identify the given coefficients for the quadratic function:

• The coefficient for $x^2$, referred to as $a$, is given as $a = -1$.
• The coefficient for $x$, referred to as $b$, is given as $b = -6$.
• The constant term, referred to as $c$, is given as $c = 9$.

Step 2: Write down the formula for the standard form of a quadratic equation:

The standard quadratic expression is given by:

$y = ax^2 + bx + c$

Step 3: Substitute the given values into the formula:

Substituting $a = -1$, $b = -6$, and $c = 9$ into the formula, we have:

$y = -1 \cdot x^2 + (-6) \cdot x + 9$

Step 4: Simplify the expression

The simplified expression becomes:

$y = -x^2 - 6x + 9$

After calculating, we match this solution to the provided answer choices. The correct choice is:

$-x^2 - 6x + 9$

Therefore, the algebraic expression based on the parameters is $-x^2 - 6x + 9$.