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

Q: Why does c = 0 make the constant term disappear?

When c = 0, adding zero doesn't change the expression! So $ -x^2 + x + 0 = -x^2 + x $. Any term multiplied by zero simply vanishes from the final expression.

Q: What if I wrote the terms in a different order?

The order doesn't matter mathematically! $ -x^2 + x $ and $ x - x^2 $ are equivalent. However, standard form puts the highest degree term first.

Q: What does it mean when a coefficient is negative?

A negative coefficient like a = -1 creates a downward-opening parabola. It literally means "negative one times x²" which gives you $ -x^2 $.

Q: Can I simplify this expression further?

No! $ -x^2 + x $ is already in simplest form. You cannot combine unlike terms (x² and x are different powers), so this is your final answer.

Quadratic Functions with Coefficient Substitution

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

00:00 Convert the parameters to a quadratic function

00:03 We'll use the formula to represent a quadratic equation

00:14 Connect the parameter to the corresponding variable according to the formula

00:32 Write the function in its simplified 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:

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

Step-by-step solution

To determine the algebraic expression, we start with the standard quadratic function:

$y = ax^2 + bx + c$

Given the values:

$a = -1$
$b = 1$
$c = 0$

We substitute these into the formula:

$y = (-1)x^2 + 1x + 0$

Simplifying the expression gives:

$y = -x^2 + x$

Thus, the algebraic expression, when these parameters are substituted, is:

The solution to the problem is $\boxed{-x^2 + x}$ .

Final Answer

$-x^2+x$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Always start with ax² + bx + c formula
Substitution: Replace a = -1, b = 1, c = 0 to get -x² + x
Verification: Check signs match: negative a makes -x², positive b makes +x ✓

Common Mistakes

Avoid these frequent errors

Forgetting to apply the negative sign to coefficient a
Don't write x² when a = -1, this ignores the negative sign = wrong expression! The negative coefficient must be applied to the entire x² term. Always write (-1)x² = -x² when substituting.

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 does c = 0 make the constant term disappear?

When c = 0, adding zero doesn't change the expression! So $-x^2 + x + 0 = -x^2 + x$ . Any term multiplied by zero simply vanishes from the final expression.

What if I wrote the terms in a different order?

The order doesn't matter mathematically! $-x^2 + x$ and $x - x^2$ are equivalent. However, standard form puts the highest degree term first.

How do I remember which coefficient goes with which term?

Use the pattern: a goes with x², b goes with x, and c is the constant. Think alphabetical order matches the decreasing powers!

What does it mean when a coefficient is negative?

A negative coefficient like a = -1 creates a downward-opening parabola. It literally means "negative one times x²" which gives you $-x^2$ .

Can I simplify this expression further?

No! $-x^2 + x$ is already in simplest form. You cannot combine unlike terms (x² and x are different powers), so this is your final answer.

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

Quadratic Functions with Coefficient Substitution

❤️ 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 c = 0 make the constant term disappear?

What if I wrote the terms in a different order?

How do I remember which coefficient goes with which term?

What does it mean when a coefficient is negative?

Can I simplify this expression further?

🌟 Unlock Your Math Potential

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