Create an Algebraic Expression: Substitute a=3, b=0, c=-3

Q: Why is the middle term missing in the final answer?

The middle term disappears because b = 0! When you substitute b = 0, you get $ 0x = 0 $, which equals zero and can be removed from the expression.

Q: Do I always need to write y = before the expression?

Not always! The question asks for an algebraic expression, so $ 3x^2 - 3 $ is sufficient. The y = part shows it's a function, but the expression itself is the key part.

Q: How do I know which coefficient goes where?

Remember the standard order: $ ax^2 + bx + c $. The coefficient of $ x^2 $ is a, the coefficient of $ x $ is b, and the constant term is c.

Q: What does it mean to 'create' an algebraic expression?

It means to build or write the expression using the given values. You're taking the general form $ ax^2 + bx + c $ and making it specific by substituting the given numbers.

Quadratic Expressions with Standard Form

Create an algebraic expression based on the following parameters:

$a=3,b=0,c=-3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's turn the parameters into a quadratic function.

00:11 Use the formula for a quadratic equation.

00:17 Connect each parameter to the right variable using the formula.

00:28 Now, write the function in its simplest form.

00:38 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Create an algebraic expression based on the following parameters:

$a=3,b=0,c=-3$

Step-by-step solution

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

$y = 3x^2 - 3$

Final Answer

$3x^2-3$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Use $ax^2 + bx + c$ format for quadratic expressions
Substitution: Replace variables with given values: $3x^2 + 0x + (-3)$
Simplification: Remove zero terms and combine: $3x^2 - 3$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to include the coefficient values properly
Don't write ax² + bx + c with letters instead of numbers = incomplete substitution! This leaves the expression in general form rather than the specific form requested. Always substitute the exact given values: a=3, b=0, c=-3 into every position.

Practice Quiz

Test your knowledge with interactive questions

Identify the coefficients based on the following equation

$$ y=x^2 $$

FAQ

Everything you need to know about this question

Why is the middle term missing in the final answer?

The middle term disappears because b = 0! When you substitute b = 0, you get $0x = 0$ , which equals zero and can be removed from the expression.

Do I always need to write y = before the expression?

Not always! The question asks for an algebraic expression, so $3x^2 - 3$ is sufficient. The y = part shows it's a function, but the expression itself is the key part.

What if one of the coefficients was a fraction?

Substitute fractions just like whole numbers! For example, if a = 1/2, you'd get $\frac{1}{2}x^2$ . The process stays exactly the same.

How do I know which coefficient goes where?

Remember the standard order: $ax^2 + bx + c$ . The coefficient of $x^2$ is a, the coefficient of $x$ is b, and the constant term is c.

What does it mean to 'create' an algebraic expression?

It means to build or write the expression using the given values. You're taking the general form $ax^2 + bx + c$ and making it specific by substituting the given numbers.

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Create an Algebraic Expression: Substitute a=3, b=0, c=-3

Quadratic Expressions with Standard Form

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is the middle term missing in the final answer?

Do I always need to write y = before the expression?

What if one of the coefficients was a fraction?

How do I know which coefficient goes where?

What does it mean to 'create' an algebraic expression?

🌟 Unlock Your Math Potential

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