Create an Algebraic Expression Using Parameters: a = -1, b = -2, c = -5

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

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

Q: How do I handle multiple negative parameters at once?

Substitute each parameter carefully one at a time: a=-1 gives $ -x^2 $, b=-2 gives $ -2x $, and c=-5 stays $ -5 $. Then combine them all together.

Q: What's the difference between -2x and (-2)x?

They're the same thing! Both equal -2x. The parentheses in (-2)x just make it clearer that we're multiplying by negative 2.

Q: Can I change the order of terms in my final answer?

Yes! $ -x^2 - 2x - 5 $ is the same as $ -5 - 2x - x^2 $, but standard form puts the highest power first, so $ -x^2 - 2x - 5 $ is preferred.

Quadratic Expressions with Negative Coefficients

Create an algebraic expression based on the following parameters:

$a=-1,b=-2,c=-5$

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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

00:10 Connect the parameter to the corresponding variable according to the formula

00:28 Write the function in its simplified form

00:44 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:

$a=-1,b=-2,c=-5$

Step-by-step solution

To create the algebraic expression for the quadratic function given the parameters, we follow these steps:

Step 1: Identify the values to substitute into the equation. Here, we have $a = -1$ , $b = -2$ , and $c = -5$ .
Step 2: Use the standard quadratic equation format $y = ax^2 + bx + c$ .
Step 3: Substitute the known values into the equation:

Substituting these values, we get:
$y = (-1)x^2 + (-2)x + (-5)$

Simplify this expression:
This simplifies to $-x^2 - 2x - 5$ .

Therefore, the algebraic expression is $-x^2 - 2x - 5$ .

Final Answer

$-x^2-2x-5$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Use $ax^2 + bx + c$ with given parameter values
Substitution: Replace a=-1, b=-2, c=-5 directly into the formula
Check: Verify all signs match: $-x^2 - 2x - 5$ has correct negative terms ✓

Common Mistakes

Avoid these frequent errors

Ignoring negative signs when substituting parameters
Don't write $x^2 + 2x + 5$ when a=-1, b=-2, c=-5 = completely wrong expression! This happens when you forget that negative parameters create negative terms. Always carefully substitute each negative value: (-1)x² becomes -x², (-2)x becomes -2x, and (-5) stays -5.

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 $ax^2$ , you get $(-1)x^2 = -x^2$ . The negative coefficient makes the entire term negative!

How do I handle multiple negative parameters at once?

Substitute each parameter carefully one at a time: a=-1 gives $-x^2$ , b=-2 gives $-2x$ , and c=-5 stays $-5$ . Then combine them all together.

What's the difference between -2x and (-2)x?

They're the same thing! Both equal -2x. The parentheses in (-2)x just make it clearer that we're multiplying by negative 2.

Can I change the order of terms in my final answer?

Yes! $-x^2 - 2x - 5$ is the same as $-5 - 2x - x^2$ , but standard form puts the highest power first, so $-x^2 - 2x - 5$ is preferred.

How can I check if my expression is correct?

Pick a simple value like x=1 and substitute it into both your expression and the original formula $ax^2 + bx + c$ . If you get the same result, you're correct!

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Create an Algebraic Expression Using Parameters: a = -1, b = -2, c = -5

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?

How do I handle multiple negative parameters at once?

What's the difference between -2x and (-2)x?

Can I change the order of terms in my final answer?

How can I check if my expression is correct?

🌟 Unlock Your Math Potential

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