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

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 $\boxed{-10x^2 + 2x}$.

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, we need to create a quadratic expression using the provided values for $a$, $b$, and $c$.

The standard form of a quadratic function is:

$y = ax^2 + bx + c$

Given the values:

• $a = 2$
• $b = 2$
• $c = 2$

We substitute these values into the standard quadratic formula:

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

Therefore, the algebraic expression for the quadratic function based on the provided parameters is $2x^2 + 2x + 2$.

The correct answer is choice 1: $2x^2 + 2x + 2$.

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, 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 $-2x^2 + 3x + 4$.

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 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 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 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 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 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 need to construct the quadratic equation using the given parameters:

• Step 1: Identify the parameters from the problem statement:
  - $a = -3$, $b = 4$, $c = -15$.
• Step 2: Apply these parameters to the standard form of a quadratic equation:
  - The standard form is $y = ax^2 + bx + c$.
• Step 3: Substitute the given values into the standard form:
  - Substitute $a = -3$, $b = 4$, $c = -15$ into $y = ax^2 + bx + c$.

By substitution, the equation becomes:

$y = -3x^2 + 4x - 15$.

This expression correctly represents the quadratic equation using the specified parameters.

Therefore, the correct answer is option 3: $-3x^2 + 4x - 15$.

To create an algebraic expression based on the parameters provided, we need to follow these steps:

• Step 1: Recognize the standard form of a quadratic function: $y = ax^2 + bx + c$.
• Step 2: Identify and substitute the given values $a = 3$, $b = 4$, and $c = -15$ into this form.
• Step 3: Substitute to form the expression: $y = 3x^2 + 4x - 15$.

Step 1: We recognize that we are dealing with a quadratic equation in the form $y = ax^2 + bx + c$.

Step 2: Using the values given in the problem statement, substitute $a = 3$, $b = 4$, and $c = -15$ into this standard form equation:

$y = ax^2 + bx + c \rightarrow y = 3x^2 + 4x - 15$

Step 3: This substitution gives us the algebraic expression:

$3x^2 + 4x - 15$

Therefore, the expression based on the given parameters is $\mathbf{3x^2 + 4x - 15}$.

To solve this problem, we will follow these steps:

• Step 1: Substitute the given values $a = -3$, $b = 15$, and $c = 0$ into the quadratic formula $ax^2 + bx + c$.
• Step 2: Simplify the expression, removing any terms where the coefficient is zero.

Let's apply these steps:

Step 1: Start with the standard form of a quadratic expression $ax^2 + bx + c$. Given $a = -3$, $b = 15$, and $c = 0$, substitute these values:

$y = -3x^2 + 15x + 0$

Step 2: Simplify the expression:

The term $+0$ can be removed because it does not affect the value of the expression, leading to:

$y = -3x^2 + 15x$

Thus, the algebraic expression based on the parameters provided is $-3x^2 + 15x$.

Among the given choices, the correct choice is:

• Choice 4: $-3x^2 + 15x$

To solve this problem, we will follow these steps:

• Step 1: Identify the given parameters $a = 3$, $b = 6$, $c = 9$.
• Step 2: Use the standard formula for a quadratic expression, which is $y = ax^2 + bx + c$.
• Step 3: Substitute the given values into this formula.

Now, let's work through each step:
Step 1: We have the parameters $a = 3$, $b = 6$, $c = 9$.
Step 2: The standard form of a quadratic equation is $y = ax^2 + bx + c$.
Step 3: Substituting the given values into the expression, we get:

$y = 3x^2 + 6x + 9$

Therefore, the algebraic expression based on the given parameters is:

$3x^2 + 6x + 9$.

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: 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 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 this problem, we need to form a quadratic expression using the given parameters.

• Step 1: Identify the given coefficients as follows: $a = 4$, $b = -2$, $c = 16$.
• Step 2: Use the standard quadratic form $ax^2 + bx + c$.
• Step 3: Substitute the given values into the quadratic form to get the expression $4x^2 - 2x + 16$.

Now, let's perform the substitution:

Substituting the values:
$a = 4$: This gives us $4x^2$.
$b = -2$: This gives us $-2x$.
$c = 16$: This remains as $+16$.

Thus, the complete quadratic expression is $4x^2 - 2x + 16$.

Therefore, the solution to the problem is $\boxed{4x^2 - 2x + 16}$.

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 $4x^2 + 2x + 5$.