Standard Form of the Quadratic Function

The goal is to express the quadratic equation $y = ax^2 + bx + c$ using the given parameters $a = -1$, $b = -1$, and $c = -1$.

First, substitute the values of $a$, $b$, and $c$ into the standard form:

• Substituting $a = -1$, the term becomes $-x^2$.
• Substituting $b = -1$, the term becomes $-x$.
• Substituting $c = -1$, the term remains $-1$.

Combine these terms to form the full expression:

$y = -x^2 - x - 1$

Therefore, the algebraic expression for the parameters $a = -1$, $b = -1$, and $c = -1$ is: $-x^2 - x - 1$.

Comparing with the given choices, the correct choice is option 4: $-x^2-x-1$

To create the algebraic expression for the quadratic function given the parameters, we follow these steps:

• Step 1: Identify the values to substitute into the equation. Here, we have $a = -1$, $b = -2$, and $c = -5$.
• Step 2: Use the standard quadratic equation format $y = ax^2 + bx + c$.
• Step 3: Substitute the known values into the equation:

Substituting these values, we get:
$y = (-1)x^2 + (-2)x + (-5)$

Simplify this expression:
This simplifies to $-x^2 - 2x - 5$.

Therefore, the algebraic expression is $-x^2 - 2x - 5$.

To derive the algebraic expression based on the parameters given, we follow these steps:

• Step 1: Recognize the given parameters: $a = 4$, $b = 2$, and $c = 5$.
• Step 2: Acknowledge that the standard form for a quadratic expression is $y = ax^2 + bx + c$.
• Step 3: Substitute the given parameter values into this quadratic expression.

Now, let's implement these steps to form the quadratic expression:
Step 1: The given parameters are $a = 4$, $b = 2$, and $c = 5$.
Step 2: Our basis is the quadratic form $y = ax^2 + bx + c$.
Step 3: Substituting the given values, we find:

$y = 4x^2 + 2x + 5$

This substitution provides us with the quadratic expression $y = 4x^2 + 2x + 5$, fulfilling the problem's requirements.

Therefore, the correct algebraic expression is $4x^2 + 2x + 5$.

To determine the algebraic expression, we start with the standard quadratic function:

$y = ax^2 + bx + c$

Given the values:

• $a = -1$
• $b = 1$
• $c = 0$

We substitute these into the formula:

$y = (-1)x^2 + 1x + 0$

Simplifying the expression gives:

$y = -x^2 + x$

Thus, the algebraic expression, when these parameters are substituted, is:

The solution to the problem is $\boxed{-x^2 + x}$.

To determine the algebraic expression, we will substitute the given parameters into the standard form of the quadratic function:

• The standard quadratic form is $y = ax^2 + bx + c$.
• Substitute $a = 1$, $b = 1$, and $c = 0$ into the equation.

Substituting these values, the expression becomes:

$y = 1 \cdot x^2 + 1 \cdot x + 0$.

This simplifies to:

$y = x^2 + x$.

Therefore, the algebraic expression, based on the given parameters, is $x^2 + x$.