Craft an Algebraic Expression Using Parameters: a = -1, b = 1, c = 2

Q: What does each parameter represent in the quadratic function?

In $ y = ax^2 + bx + c $, a is the coefficient of $ x^2 $, b is the coefficient of $ x $, and c is the constant term.

Q: Why is the answer $ -x^2 + x + 2 $ and not $ x^2 + x + 2 $ ?

Because a = -1, not +1! The negative sign is crucial. When we substitute a = -1, we get $ (-1) \cdot x^2 = -x^2 $.

Q: Do I need to write the 1 in front of x?

No, $ 1 \cdot x $ is simply written as $ x $. The coefficient 1 is implied and doesn't need to be written explicitly.

Q: What if one of the parameters was 0?

If a = 0, it's not quadratic anymore (it becomes linear). If b = 0, you get $ ax^2 + c $. If c = 0, you get $ ax^2 + bx $.

Q: How do I check my work?

Verify that each term matches: the $ x^2 $ coefficient should be a, the $ x $ coefficient should be b, and the constant should be c.

Quadratic Functions with Given Parameters

Create an algebraic expression based on the following parameters:

$a=-1,b=1,c=2$

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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

00:09 Connect the parameter to the corresponding variable according to the formula

00:25 Write the function in its reduced form

00:34 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:

$a=-1,b=1,c=2$

Step-by-step solution

First, we review our quadratic function formula: $y = ax^2 + bx + c$ .

To create the expression:

We substitute $a = -1$ , $b = 1$ , and $c = 2$ into the expression.
This results in: $y = -1 \cdot x^2 + 1 \cdot x + 2$ .
Simplifying, we have: $y = -x^2 + x + 2$ .

Thus, the algebraic expression is: $-x^2 + x + 2$ .

Final Answer

$-x^2+x+2$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Use the general formula $y = ax^2 + bx + c$
Substitution: Replace a = -1, b = 1, c = 2 into the formula
Verification: Check that $-x^2 + x + 2$ matches the coefficients ✓

Common Mistakes

Avoid these frequent errors

Forgetting negative signs when substituting parameters
Don't write $x^2 + x + 2$ when a = -1 = wrong leading coefficient! This ignores the negative value of parameter a. Always carefully substitute each parameter with its correct sign into $ax^2 + bx + c$ .

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

What does each parameter represent in the quadratic function?

In $y = ax^2 + bx + c$ , a is the coefficient of $x^2$ , b is the coefficient of $x$ , and c is the constant term.

Why is the answer $-x^2 + x + 2$ and not $x^2 + x + 2$ ?

Because a = -1, not +1! The negative sign is crucial. When we substitute a = -1, we get $(-1) \cdot x^2 = -x^2$ .

Do I need to write the 1 in front of x?

No, $1 \cdot x$ is simply written as $x$ . The coefficient 1 is implied and doesn't need to be written explicitly.

What if one of the parameters was 0?

If a = 0, it's not quadratic anymore (it becomes linear). If b = 0, you get $ax^2 + c$ . If c = 0, you get $ax^2 + bx$ .

How do I check my work?

Verify that each term matches: the $x^2$ coefficient should be a, the $x$ coefficient should be b, and the constant should be c.

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Craft an Algebraic Expression Using Parameters: a = -1, b = 1, c = 2

Quadratic Functions with Given Parameters

❤️ 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 each parameter represent in the quadratic function?

Why is the answer $-x^2 + x + 2$ and not $x^2 + x + 2$ ?

Do I need to write the 1 in front of x?

What if one of the parameters was 0?

How do I check my work?

🌟 Unlock Your Math Potential

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Quadratic Functions with Given Parameters

❤️ 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 each parameter represent in the quadratic function?

Why is the answer −x2+x+2 -x^2 + x + 2 −x2+x+2 and not x2+x+2 x^2 + x + 2 x2+x+2?

Do I need to write the 1 in front of x?

What if one of the parameters was 0?

How do I check my work?

🌟 Unlock Your Math Potential

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