Formulate an Algebraic Expression: Given a=1, b=-1, c=1

Q: What does the standard quadratic form mean?

The standard quadratic form is $ ax^2 + bx + c $ where a, b, and c are coefficients. It's like a template you fill in with given values!

Q: How do I handle the coefficient of 1 for x²?

When $ a = 1 $, you can write either $ 1x^2 $ or just $ x^2 $. Both are correct, but $ x^2 $ is the simplified form.

Quadratic Expressions with Given Coefficients

Create an algebraic expression based on the following parameters:

$a=1,b=-1,c=1$

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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 Use the formula to represent a quadratic equation

00:08 Connect the parameter to its corresponding unknown according to the formula

00:22 Write the function in its reduced form

00:30 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:

$a=1,b=-1,c=1$

Step-by-step solution

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: $x^2-x+1$

Final Answer

$x^2-x+1$

Key Points to Remember

Essential concepts to master this topic

Formula: Standard quadratic form is $ax^2 + bx + c$
Technique: Substitute given values: $1x^2 + (-1)x + 1$
Check: Simplify carefully: $x^2 - x + 1$ matches option 3 ✓

Common Mistakes

Avoid these frequent errors

Confusing signs when substituting negative coefficients
Don't write $x^2 + (-1)x$ as $x^2 + -x$ = messy notation! This leads to sign errors and wrong expressions. Always simplify $+(-1)x$ to $-x$ immediately.

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

What does the standard quadratic form mean?

The standard quadratic form is $ax^2 + bx + c$ where a, b, and c are coefficients. It's like a template you fill in with given values!

Why is b = -1 written as +(-1) in the substitution?

When substituting, we replace b with its exact value. Since $b = -1$ , we write $bx = (-1)x$ . This helps avoid sign errors during simplification.

How do I handle the coefficient of 1 for x²?

When $a = 1$ , you can write either $1x^2$ or just $x^2$ . Both are correct, but $x^2$ is the simplified form.

What if I chose the wrong answer option?

Check your signs carefully! The most common error is getting $x^2 - x - 1$ instead of $x^2 - x + 1$ . Remember that c = +1, not -1.

Can I verify my expression is correct?

Yes! Pick any x-value (like x = 0) and substitute into your expression. For $x^2 - x + 1$ with x = 0: $0 - 0 + 1 = 1$ . This matches c = 1! ✓

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Formulate an Algebraic Expression: Given a=1, b=-1, c=1

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

What does the standard quadratic form mean?

Why is b = -1 written as +(-1) in the substitution?

How do I handle the coefficient of 1 for x²?

What if I chose the wrong answer option?

Can I verify my expression is correct?

🌟 Unlock Your Math Potential

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