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

To solve this problem, we will substitute the given values into the standard quadratic form:

• Step 1: Identify the formula to use. We need the standard form of a quadratic function, which is $y = ax^2 + bx + c$.
• Step 2: Substitute the given parameters into the formula:
  $a = -3$, $b = 3$, and $c = 7$.
• Step 3: Perform the substitution:
  Substituting in, we get $y = -3x^2 + 3x + 7$.

Therefore, the correct algebraic expression is $-3x^2 + 3x + 7$.

This corresponds to choice 2 of the multiple-choice options provided.

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:

$y = 0 + x + 0$

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

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

To solve this problem, we must recognize that we are given parameters for a quadratic function defined by the expression $y = ax^2 + bx + c$.

Given:

• $a = 0$
• $b = 2$
• $c = 4$

Step 1: Start with the general form of a quadratic function: $y = ax^2 + bx + c$.

Step 2: Substitute the given values of $a$, $b$, and $c$ into the expression.

So, we have:

$y = 0 \cdot x^2 + 2x + 4$

Step 3: Simplify the expression.

The term $0 \cdot x^2$ equals 0, and therefore, it drops out of the expression. This results in:

$y = 2x + 4$

This is the algebraic expression based on the parameters provided. Thus, the correct choice from the options given is:

$2x + 4$, which corresponds to choice $2$.

To solve this problem, we will create an algebraic expression by following these steps:

• Step 1: Identify the standard form of a quadratic function, $y = ax^2 + bx + c$.
• Step 2: Substitute the given values $a = -10$, $b = 2$, and $c = 0$ into the formula.
• Step 3: Simplify the resulting expression.

Let's apply these steps:

Step 1: The standard quadratic function format is given as $y = ax^2 + bx + c$.

Step 2: Substitute the given values:

$y = (-10)x^2 + 2x + 0$

Step 3: Simplify the expression by removing the zero term (as $c = 0$ and it has no impact on the expression):

$y = -10x^2 + 2x$

This simplified expression $y = -10x^2 + 2x$ is the required algebraic representation based on the given parameters.

Therefore, the correct algebraic expression for the parameters $a = -10$, $b = 2$, and $c = 0$ is $\boxed{-10x^2 + 2x}$.

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 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:

$-x^2-16x-64$

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 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 $x^2 + x$.

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 follow these steps:

• Step 1: Identify the provided coefficients for the expression of the form $ax^2 + bx + c$.
• Step 2: Substitute the provided values into the expression.

Now, let's perform these steps:

Step 1: The problem provides us with the coefficients $a = 1$, $b = -1$, and $c = 3$ for a quadratic expression $ax^2 + bx + c$.

Step 2: Substitute these values into the quadratic expression:

$a = 1$: Multiply $x^2$ by $1$, resulting in $x^2$.

$b = -1$: Multiply $x$ by $-1$, resulting in $-x$.

$c = 3$: The constant term is $3$.

Thus, the algebraic expression is:

$x^2 - x + 3$.

Comparing this result to the given choices, we find that this expression matches choice 3.

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

To formulate the quadratic expression using the given parameters, we follow these steps:

• Step 1: Identify the formula: The standard form of a quadratic function is $y = ax^2 + bx + c$.
• Step 2: Substitute the values: Insert $a = -1$, $b = 2$, and $c = 0$ into the formula.
• Step 3: Simplify the expression: Apply the values directly and simplify where necessary.

Here’s how we perform each step:
Step 1: We start with the formula: $y = ax^2 + bx + c$.
Step 2: Substitute the given values: $y = (-1)x^2 + 2x + 0$.
Step 3: This simplifies to $y = -x^2 + 2x$ since adding zero does not change the expression.

Thus, the algebraic expression representing the quadratic function with the given parameters is $y = -x^2 + 2x$.

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: $x^2 + 2x$.

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 will derive the algebraic expression step-by-step:

Step 1: Identify the given information:
The problem states $a = 2$, $b = 0$, and $c = 4$.

Step 2: Write the standard quadratic expression:
The general form is $y = ax^2 + bx + c$.

Step 3: Substitute the given values into the expression:
Replace $a$ with 2, $b$ with 0, and $c$ with 4:
$y = 2x^2 + 0x + 4$.

Step 4: Simplify the expression:
Since $0x$ is zero, the expression simplifies to:
$y = 2x^2 + 4$.

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

The correct answer is: $2x^2 + 4$ (Choice 1).

To solve this problem, we will construct an algebraic expression using the given parameters in a quadratic function format.

• Step 1: Identify the formula required. The standard quadratic function is given by $ax^2 + bx + c$.
• Step 2: Substitute the given values of $a$, $b$, and $c$. We have $a = 2$, $b = 0$, and $c = 6$.
• Step 3: Insert these values into the formula: $2x^2 + 0x + 6$.
• Step 4: Simplify the expression. Since the coefficient of $x$ is zero, $0x$ can be omitted. This simplifies the expression to $2x^2 + 6$.

The final algebraic expression, representing the given parameters in a quadratic form, is $2x^2 + 6$.

Therefore, the correct algebraic expression is $2x^2 + 6$.

To solve this problem, we need to form an algebraic expression for a quadratic function using given parameters.

We start by recalling the standard form of a quadratic function: $( ax^2 + bx + c )$. In this expression:

• $a$ is the coefficient of $x^2$
• $b$ is the coefficient of $x$
• $c$ is the constant term

Given the values are $a = 2$, $b = 4$, and $c = 8$, we substitute these into the standard form equation:

$ax^2 + bx + c = 2x^2 + 4x + 8$

This yields the algebraic expression for the quadratic function.

The correct expression, given all calculations and simplifications, is $2x^2 + 4x + 8$.

Referring to the choices provided, the correct choice is:

: $( 2x^2 + 4x + 8 )$

Therefore, the solution to the problem is $\boxed{2x^2 + 4x + 8}$.

To solve this problem, we'll follow the steps outlined:

• Step 1: Identify the given values for the quadratic function's parameters: $a = 2$, $b = \frac{1}{2}$, and $c = 4$.
• Step 2: Apply these values to the standard quadratic form $y = ax^2 + bx + c$.
• Step 3: Substitute the values to construct the algebraic expression.

Now, let's proceed with these steps:

Given the standard form of a quadratic expression $y = ax^2 + bx + c$:

Substituting the values, we obtain:

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

Therefore, the correct algebraic expression for the quadratic function is $2x^2 + \frac{1}{2}x + 4$.

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 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

$y = 3x^2 - 3$