The function y=ax²+bx+c: Determine the algebraic representation of the following descriptions

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 $-x^2 - 6x + 9$.

To solve this problem, we'll follow these steps:

• Step 1: Substitute the given values $a = 3$, $b = 0$, and $c = 0$ into the quadratic function formula $y = ax^2 + bx + c$.
• Step 2: Simplify the expression.

Let's execute these steps:

Step 1: Substitute the values into the formula:
$y = 3x^2 + 0x + 0$

Step 2: Simplify the expression:
Eliminate the terms with zero coefficients to get:
$y = 3x^2$

Thus, the algebraic expression for the quadratic function with $a = 3$, $b = 0$, and $c = 0$ is $3x^2$.

Therefore, the correct choice from the options provided is choice 1: $3x^2$

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 $x^2 + x$.

To solve this problem, follow these steps:

• Step 1: Identify the given parameters from the problem statement. We have $a = -2$, $b = 3$, and $c = 4$.
• Step 2: Substitute these values into the standard quadratic formula $y = ax^2 + bx + c$.
• Step 3: Write the algebraic expression using the substituted values.

Now let's execute these steps:

Step 1: We know $a = -2$, $b = 3$, and $c = 4$.

Step 2: Substitute the values into the quadratic function:

$y = (-2)x^2 + (3)x + 4$

Step 3: Simplify to present the function:

The algebraic expression is $y = -2x^2 + 3x + 4$.

Therefore, the solution to the problem is $-2x^2 + 3x + 4$.

We begin by noting that the general form of a quadratic function is represented by the equation:

$y = ax^2 + bx + c$

Given the parameters $a = -1$, $b = 0$, and $c = 0$, we substitute these values into the equation:

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

Simplifying the expression, we get:

$y = -x^2$

Thus, the algebraic expression representing the given parameters is $-x^2$.

The correct answer choice that corresponds to this expression is:

$-x^2$

To solve this problem, we need to form a quadratic expression using given parameters in the standard form:

The standard quadratic function is represented as:

• $y = ax^2 + bx + c$

Given parameters are:

• $a = 4$
• $b = 2$
• $c = \frac{1}{2}$

We substitute these values into the standard quadratic expression:

$y = 4x^2 + 2x + \frac{1}{2}$

Thus, the algebraic expression we are looking for is $4x^2 + 2x + \frac{1}{2}$.

Among the provided answer choices, the correct choice is:

• Choice 3: $4x^2 + 2x + \frac{1}{2}$

The expression $4x^2 + 2x + \frac{1}{2}$ accurately represents the quadratic function with the given parameters.

To solve this problem, we'll utilize the standard form of a quadratic function given by:

$y = ax^2 + bx + c$

Let's proceed with the given values for the parameters:

• $a = 2$

• $b = 0$

• $c = 0$

Substitute these values into the quadratic function formula:

$y = 2x^2 + 0x + 0$

Simplify the expression by removing terms with zero coefficients:

$y = 2x^2$

Hence, the algebraic representation of the quadratic function with the given parameters is $2x^2$.

After reviewing the answer choices, the correct choice is:

$2x^2$

To solve the problem, we will create an algebraic expression using the specified parameters.

• Step 1: Start with the general form of a quadratic expression: $y = ax^2 + bx + c$.
• Step 2: Substitute the given values ($a = -1$, $b = -16$, $c = -64$) into the form. This yields: $y = -1x^2 - 16x - 64$.
• Step 3: Simplify the expression. Since the terms are already simplified, the expression remains: $y = -x^2 - 16x - 64$.

Therefore, the algebraic expression based on the given parameters is $-x^2 - 16x - 64$.

Final solution: The correct answer is $-x^2 - 16x - 64$.

Among the given choices, this corresponds to choice 4:

$-x^2-16x-64$

First, we review our quadratic function formula: $y = ax^2 + bx + c$.

To create the expression:

• We substitute $a = -1$, $b = 1$, and $c = 2$ into the expression.
• This results in: $y = -1 \cdot x^2 + 1 \cdot x + 2$.
• Simplifying, we have: $y = -x^2 + x + 2$.

Thus, the algebraic expression is: $-x^2 + x + 2$.

To solve this problem, we'll start by substituting the given parameters into the standard quadratic formula:

$y = ax^2 + bx + c$

The problem gives us the values:

• $a = -1$
• $b = -8$
• $c = 0$

This means we need to replace $a$, $b$, and $c$ in the formula:

$y = (-1)x^2 + (-8)x + 0$

Simplifying this expression further:

• The term with $a$: (-1)x^2\) results in $-x^2$.
• The term with $b$: (-8)x\) simplifies to $-8x$.
• The term with $c$: $0$ contributes nothing to the expression, so it is omitted.

Thus, the final algebraic expression is:

$y = -x^2 - 8x$

Therefore, the algebraic expression based on the given parameters is

$-x^2 - 8x$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the general form of the quadratic expression.
• Step 2: Substitute the given values $a = 5$, $b = 3$, and $c = -4$ into the quadratic form.
• Step 3: Write down the resultant expression.

Now, let's work through each step:
Step 1: The general form of a quadratic expression is $ax^2 + bx + c$.
Step 2: We are given $a = 5$, $b = 3$, and $c = -4$. Substituting these into the expression, we get:

$5x^2 + 3x - 4$

Therefore, the solution to the problem is $5x^2 + 3x - 4$.

To solve this problem, we'll use the following steps:

• Step 1: Substitute $a = 0$, $b = 1$, $c = 0$ into the quadratic equation $y = ax^2 + bx + c$.
• Step 2: Simplify the expression based on these substitutions.

Working through these steps:

Step 1: Start with the expression $y = ax^2 + bx + c$.

Since $a = 0$, then $ax^2 = 0 \cdot x^2 = 0$.
Since $b = 1$, then $bx = 1 \cdot x = x$.
Since $c = 0$, then $c = 0$.

Step 2: Plug these values into the equation:

The expression simplifies to:

Thus, the simplified algebraic expression is $y = x$.

Therefore, the solution to the problem is $x$.

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

• Step 1: Identify the quadratic function format: $y = ax^2 + bx + c$.
• Step 2: Substitute the given values $a = 4$, $b = 0$, and $c = 2$ into the formula.
• Step 3: The expression becomes $y = 4x^2 + 0x + 2$.
• Step 4: Simplify the expression by removing the term with the zero coefficient: $y = 4x^2 + 2$.

Therefore, the solution to this problem is $4x^2 + 2$.

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 solve the problem, we need to substitute the given coefficients into the standard form of a quadratic function.

• Step 1: Identify the coefficients from the problem parameters: $a = 3$, $b = 0$, $c = \frac{1}{3}$.
• Step 2: Substitute these values into the quadratic expression $ax^2 + bx + c$. This gives us $3x^2 + 0 \cdot x + \frac{1}{3}$.
• Step 3: Simplify the expression by removing the term with $0 \cdot x$, resulting in $3x^2 + \frac{1}{3}$.

Thus, the algebraic expression for the given parameters is $3x^2 + \frac{1}{3}$.

To solve this problem, we'll follow these steps:

• Step 1: Formulate using the standard quadratic expression template.
• Step 2: Substitute the given parameters.
• Step 3: Simplify the resultant expression.

Now, let's work through each step:

Step 1: We use the standard form of a quadratic expression, which is $ax^2 + bx + c$.

Step 2: Substitute the values $a = 4$, $b = -16$, and $c = 0$ into this template:

$ax^2 + bx + c \rightarrow 4x^2 - 16x + 0$

Step 3: Simplify the expression:

The expression simplifies to $4x^2 - 16x$.

Thus, the algebraic expression based on the given parameters is $4x^2 - 16x$.

Checking against the answer choices, the correct choice is: $4x^2 - 16x$ .

To solve the problem of creating an algebraic expression with the given parameters, we will proceed as follows:

• Step 1: Identify the given coefficients for the quadratic function, which are $a = 3$, $b = 0$, and $c = -3$.
• Step 2: Substitute these values into the standard quadratic expression $y = ax^2 + bx + c$.

Through substitution, the expression becomes:

$y = 3x^2 + 0x - 3$

We can further simplify this expression:

$y = 3x^2 - 3$

Thus, the algebraic expression with the given parameters is $y = 3x^2 - 3$.

The correct answer corresponds to choice number 1: $3x^2-3$.

Therefore, the solution to the problem is

$y = 3x^2 - 3$

To solve this problem, we'll follow these steps:

• Step 1: Identify and substitute the values of $a$, $b$, and $c$ into the equation $y = ax^2 + bx + c$.
• Step 2: Simplify the equation to obtain the required expression.
• Step 3: Compare the simplified expression with the provided multiple-choice answers.

Let's work through each step:

Step 1: The given coefficients are $a = \frac{1}{2}$, $b = \frac{1}{2}$, and $c = \frac{1}{2}$. Substitute these values into the standard quadratic form $y = ax^2 + bx + c$:

$y = \frac{1}{2}x^2 + \frac{1}{2}x + \frac{1}{2}$

Step 2: The expression is already simplified. The coefficients are correctly substituted, and no further simplification is needed:

$y = \frac{x^2}{2} + \frac{x}{2} + \frac{1}{2}$

Step 3: Compare this expression to the provided multiple-choice options. The correct match is:

Choice 1: $\frac{x^2}{2} + \frac{x}{2} + \frac{1}{2}$

Therefore, the algebraic expression is $\frac{x^2}{2} + \frac{x}{2} + \frac{1}{2}$.

To solve this problem, let's proceed with the construction of the quadratic expression:

• Step 1: Recognize the standard form of a quadratic expression, which is $ax^2 + bx + c$.
• Step 2: Substitute the given values into this formula:
  • $a = 1$
  • $b = 16$
  • $c = 64$
  Plugging in these values, we determine the expression to be $1x^2 + 16x + 64$, which simplifies to $x^2 + 16x + 64$.

Thus, the algebraic expression we derive from these parameters is the quadratic expression:

$x^2 + 16x + 64$

This matches the correct choice provided in the given multiple-choice options.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information
• Step 2: Apply the standard quadratic formula
• Step 3: Perform the substitution

Now, let's work through each step:
Step 1: We are given $a = 1$, $b = 2$, and $c = 0$.
Step 2: We'll use the formula $y = ax^2 + bx + c$ to form our expression.
Step 3: By substituting the given values, we get:

• Replace $a$ with 1: $1x^2 = x^2$.
• Replace $b$ with 2: $2x = 2x$.
• Replace $c$ with 0: since $c = 0$, it does not contribute to the expression, so we can omit this term.

Therefore, we combine the terms to form the expression: $x^2 + 2x$.

The correct answer choice based on our derived expression is: $x^2 + 2x$.