Standard Form Quadratic Function Practice Problems

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 $x^2 + x$.

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'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 $5x^2 + 3x - 4$.