Standard Form Quadratic Function Practice Problems

The goal is to express the quadratic equation $y = ax^2 + bx + c$ using the given parameters $a = -1$, $b = -1$, and $c = -1$.

First, substitute the values of $a$, $b$, and $c$ into the standard form:

• Substituting $a = -1$, the term becomes $-x^2$.
• Substituting $b = -1$, the term becomes $-x$.
• Substituting $c = -1$, the term remains $-1$.

Combine these terms to form the full expression:

$y = -x^2 - x - 1$

Therefore, the algebraic expression for the parameters $a = -1$, $b = -1$, and $c = -1$ is: $-x^2 - x - 1$.

Comparing with the given choices, the correct choice is option 4: $-x^2-x-1$

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, let's form the algebraic expression using the standard quadratic formula:

$y = ax^2 + bx + c$

Given are the values:
$a = 1$,
$b = -1$,
$c = 1$.

Substituting these values into the formula, we have:
$y = 1 \cdot x^2 + (-1) \cdot x + 1$

This simplifies to:
$y = x^2 - x + 1$

Thus, the algebraic expression is $\boldsymbol{x^2 - x + 1}$.

The correct choice from the given options is:

Choice 3: $x^2-x+1$

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: 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: $3x^2$