Create an Algebraic Expression with a = -1, b = -1, c = -1

Q: Why does a = -1 make the x² term negative?

When you substitute a = -1 into ax², you get $ (-1) \cdot x^2 = -x^2 $. The negative coefficient makes the entire term negative!

Q: Do I need to include the y = part in my answer?

Not for this question! You're asked for the algebraic expression, which is just the right side: $ -x^2 - x - 1 $. The "y =" shows it's a function, but isn't part of the expression itself.

Q: How do I remember the order of terms?

Standard form is always highest degree first: $ ax^2 $ (degree 2), then $ bx $ (degree 1), then $ c $ (degree 0). Think: big to small!

Q: What if all my coefficients are positive instead?

Then you'd get $ +x^2 + x + 1 $ or simply $ x^2 + x + 1 $. The process is identical - just substitute the given values for a, b, and c!

Quadratic Expressions with Negative 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 from parameters to quadratic function

00:03 Use the formula to represent a quadratic equation

00:16 Connect the parameter to its corresponding variable

00:38 Write the equation in 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:

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

Step-by-step solution

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: $-x^2-x-1$

Final Answer

$-x^2-x-1$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic expressions follow ax² + bx + c pattern
Substitution: Replace a = -1: (-1)x² becomes -x², b = -1: (-1)x becomes -x
Verification: Check each term matches: -x² (first), -x (second), -1 (constant) ✓

Common Mistakes

Avoid these frequent errors

Forgetting negative signs when substituting
Don't write +x when b = -1 or +1 when c = -1 = wrong expression! Negative coefficients create negative terms in the final expression. Always preserve the negative signs when substituting values.

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 a = -1 make the x² term negative?

When you substitute a = -1 into ax², you get $(-1) \cdot x^2 = -x^2$ . The negative coefficient makes the entire term negative!

What's the difference between -x and (-1)x?

They're exactly the same! -x is just the simplified way to write (-1)x. Both mean "negative one times x".

Do I need to include the y = part in my answer?

Not for this question! You're asked for the algebraic expression, which is just the right side: $-x^2 - x - 1$ . The "y =" shows it's a function, but isn't part of the expression itself.

How do I remember the order of terms?

Standard form is always highest degree first: $ax^2$ (degree 2), then $bx$ (degree 1), then $c$ (degree 0). Think: big to small!

What if all my coefficients are positive instead?

Then you'd get $+x^2 + x + 1$ or simply $x^2 + x + 1$ . The process is identical - just substitute the given values for a, b, and c!

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Create an Algebraic Expression with a = -1, b = -1, c = -1

Quadratic Expressions with Negative 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 a = -1 make the x² term negative?

What's the difference between -x and (-1)x?

Do I need to include the y = part in my answer?

How do I remember the order of terms?

What if all my coefficients are positive instead?

🌟 Unlock Your Math Potential

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