Craft an Expression Using Variables: Where a=0, b=1, c=0

Q: Why does the x² term disappear completely?

When a = 0, the term becomes $ 0 \cdot x^2 = 0 $. Since multiplying by zero always gives zero, this entire term vanishes from the expression!

Q: Is x the same as 1x?

Yes! When the coefficient is 1, we usually don't write it. So $ 1x $ is simplified to just $ x $. It's like saying "1 apple" vs "apple" - same meaning!

Q: How do I know which terms to keep and which to remove?

Keep any term that doesn't equal zero. Remove terms that multiply to zero (like $ 0x^2 $) or add zero (like $ +0 $).

Quadratic Expressions with Zero Coefficients

Create an algebraic expression based on the following parameters:

$a=0,b=1,c=0$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert the parameters to a quadratic function

00:03 Let's use the formula to represent a quadratic equation

00:11 Connect the parameter to its corresponding variable according to the formula

00:29 Write the function in its reduced form

00:43 And this is the solution to the question

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:

$a=0,b=1,c=0$

Step-by-step solution

To solve this problem, we'll use the following steps:

Step 1: Substitute $a = 0$ , $b = 1$ , $c = 0$ into the quadratic equation $y = ax^2 + bx + c$ .
Step 2: Simplify the expression based on these substitutions.

Working through these steps:

Step 1: Start with the expression $y = ax^2 + bx + c$ .

Since $a = 0$ , then $ax^2 = 0 \cdot x^2 = 0$ .
Since $b = 1$ , then $bx = 1 \cdot x = x$ .
Since $c = 0$ , then $c = 0$ .

Step 2: Plug these values into the equation:

The expression simplifies to:

y = 0 + x + 0

Thus, the simplified algebraic expression is $y = x$ .

Therefore, the solution to the problem is $x$ .

Final Answer

$x$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Use $y = ax^2 + bx + c$ as the template
Substitution: Replace a=0, b=1, c=0 to get $0x^2 + 1x + 0$
Simplify: Remove zero terms: $0x^2 + x + 0 = x$ ✓

Common Mistakes

Avoid these frequent errors

Keeping zero terms in the final expression
Don't write $0x^2 + x + 0$ as your final answer = unnecessarily complex! Zero terms don't affect the value but make expressions messy. Always remove terms that equal zero to get the simplest form.

Practice Quiz

Test your knowledge with interactive questions

What is the value of the coefficient $$ b $$ in the equation below?

$$ 3x^2+8x-5 $$

FAQ

Everything you need to know about this question

Why does the x² term disappear completely?

When a = 0, the term becomes $0 \cdot x^2 = 0$ . Since multiplying by zero always gives zero, this entire term vanishes from the expression!

Is x the same as 1x?

Yes! When the coefficient is 1, we usually don't write it. So $1x$ is simplified to just $x$ . It's like saying "1 apple" vs "apple" - same meaning!

What if all three coefficients were zero?

If a=0, b=0, and c=0, then the entire expression would equal 0. This would be $y = 0$ , which represents a horizontal line on the x-axis.

Can I write the answer as y = x instead of just x?

Both are correct! The question asks for an "algebraic expression," so $x$ is the expression itself. Writing $y = x$ shows the full equation.

How do I know which terms to keep and which to remove?

Keep any term that doesn't equal zero. Remove terms that multiply to zero (like $0x^2$ ) or add zero (like $+0$ ).

🌟 Unlock Your Math Potential

Get unlimited access to all 18 The Quadratic Function questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Craft an Expression Using Variables: Where a=0, b=1, c=0

Quadratic Expressions with Zero Coefficients

❤️ 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 does the x² term disappear completely?

Is x the same as 1x?

What if all three coefficients were zero?

Can I write the answer as y = x instead of just x?

How do I know which terms to keep and which to remove?

🌟 Unlock Your Math Potential

More Questions

The function y=ax²+bx+c

Constructing an Algebraic Expression: Parameters a = -1, b = 0, c = 0 Explained

Developing an Algebraic Expression: Substitute Values a=-10, b=2, c=0

Crafting an Algebraic Expression with a=3, b=0, and c=1/3

Formulate an Algebraic Expression with Constants: a=2, b=1/2, c=4

Standard Representation

The Algebraic Expression Challenge: Formulate Using a=3, b=6, c=9

Create an Algebraic Expression with Parameters: a=2, b=0, c=6

Crafting an Algebraic Expression Using the Parameters a = -1, b = 1, c = 0

Formulate an Algebraic Expression with Parameters: a=0, b=2, c=4

Plotting Functions with Parameters

Constructing an Algebraic Expression: Using a = 4, b = 2, c = 1/2

Specific Algebra Task: Create an Expression with a = -3, b = 15, c = 0

Create Algebraic Expressions: Using a=4, b=-16, c=0

Develop an Algebraic Expression Using a=3, b=4, c=-15