Standard Form Quadratic Function Practice Problems

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, 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 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

$y = 3x^2 - 3$