Construct an Algebraic Expression Using a=1, b=1, c=0

Q: Why don't we write the coefficient 1 in front of x²?

In algebra, we don't write coefficients of 1 because they're understood. Writing $ 1x^2 $ is the same as $ x^2 $, but the simpler form is preferred.

Q: Do I need to include the +0 term?

No! Adding zero to any expression doesn't change its value. When c=0, simply omit that term entirely from your final answer.

Q: Is x² + x the same as x(x + 1)?

Yes! These are equivalent expressions. $ x^2 + x = x(x + 1) $ by factoring out the common factor x.

Q: Can I write this expression in a different order?

Technically yes, but standard form puts terms in descending order of powers: $ x^2 + x $ rather than $ x + x^2 $.

Quadratic Expressions with Given Coefficients

Create an algebraic expression based on the following parameters:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's start by converting the parameters into a quadratic function.

00:13 Next, we'll use the quadratic formula to lay out our equation.

00:23 Now, match each parameter to its variable in the formula.

00:43 Then, simplify the function to its simplest form.

00:49 And there you go, that's our final solution!

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:

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

Step-by-step solution

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 $x^2 + x$ .

Final Answer

$x^2+x$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic expressions follow $ax^2 + bx + c$ pattern
Substitution: Replace a=1, b=1, c=0 to get $1x^2 + 1x + 0$
Simplify: Remove coefficient 1 and zero term: $x^2 + x$ ✓

Common Mistakes

Avoid these frequent errors

Including the zero term in final expression
Don't write $x^2 + x + 0$ as your final answer = unnecessary complexity! Adding zero doesn't change the value but makes the expression look incomplete. Always simplify by removing zero terms and coefficients of 1.

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 don't we write the coefficient 1 in front of x²?

In algebra, we don't write coefficients of 1 because they're understood. Writing $1x^2$ is the same as $x^2$ , but the simpler form is preferred.

Do I need to include the +0 term?

No! Adding zero to any expression doesn't change its value. When c=0, simply omit that term entirely from your final answer.

What if all three coefficients were different numbers?

You'd substitute all three values! For example, if a=2, b=-3, c=5, you'd get $2x^2 - 3x + 5$ . The process stays the same.

Is x² + x the same as x(x + 1)?

Yes! These are equivalent expressions. $x^2 + x = x(x + 1)$ by factoring out the common factor x.

Can I write this expression in a different order?

Technically yes, but standard form puts terms in descending order of powers: $x^2 + x$ rather than $x + x^2$ .

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Construct an Algebraic Expression Using a=1, b=1, c=0

Quadratic Expressions with Given 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 don't we write the coefficient 1 in front of x²?

Do I need to include the +0 term?

What if all three coefficients were different numbers?

Is x² + x the same as x(x + 1)?

Can I write this expression in a different order?

🌟 Unlock Your Math Potential

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