Constructing an Algebraic Expression with Constants: a = -1, b = -16, c = -64

Q: Why do all three terms have negative signs in the answer?

Because all three given values are negative! When a = -1, the $ x^2 $ term becomes negative. When b = -16 and c = -64, those terms stay negative too.

Q: What if I wrote -1x² instead of -x²?

Both are mathematically correct! We typically write $ -x^2 $ because the coefficient -1 is understood when we see a negative sign in front of a variable.

Q: How do I know this is the standard form?

The standard form for quadratic expressions is $ ax^2 + bx + c $. We arrange terms from highest to lowest degree: $ x^2 $ term first, then $ x $ term, then constant.

Q: What if I mixed up which coefficient goes where?

Remember the pattern: a always goes with $ x^2 $, b goes with $ x $, and c is the constant term (no variable). Double-check your substitution!

Quadratic Expressions with Negative Coefficients

Create an algebraic expression based on the following parameters:

$a=-1,b=-16,c=-64$

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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

00:11 We'll connect the parameter to its corresponding variable according to the formula

00:34 We'll write the function in its reduced form

00:42 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:

$a=-1,b=-16,c=-64$

Step-by-step solution

To solve the problem, we will create an algebraic expression using the specified parameters.

Step 1: Start with the general form of a quadratic expression: $y = ax^2 + bx + c$ .
Step 2: Substitute the given values ( $a = -1$ , $b = -16$ , $c = -64$ ) into the form. This yields: $y = -1x^2 - 16x - 64$ .
Step 3: Simplify the expression. Since the terms are already simplified, the expression remains: $y = -x^2 - 16x - 64$ .

Therefore, the algebraic expression based on the given parameters is $-x^2 - 16x - 64$ .

Final solution: The correct answer is $-x^2 - 16x - 64$ .

Among the given choices, this corresponds to choice 4:

$-x^2-16x-64$

Final Answer

$-x^2-16x-64$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic expressions follow $ax^2 + bx + c$ pattern
Substitution: Replace a=-1, b=-16, c=-64 to get $-x^2 - 16x - 64$
Verification: Check each term matches the given coefficients exactly ✓

Common Mistakes

Avoid these frequent errors

Forgetting negative signs when substituting
Don't write $x^2 + 16x + 64$ when a=-1, b=-16, c=-64 = completely wrong signs! This ignores the negative values entirely. Always keep the negative signs: $-x^2 - 16x - 64$ .

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 do all three terms have negative signs in the answer?

Because all three given values are negative! When a = -1, the $x^2$ term becomes negative. When b = -16 and c = -64, those terms stay negative too.

What if I wrote -1x² instead of -x²?

Both are mathematically correct! We typically write $-x^2$ because the coefficient -1 is understood when we see a negative sign in front of a variable.

How do I know this is the standard form?

The standard form for quadratic expressions is $ax^2 + bx + c$ . We arrange terms from highest to lowest degree: $x^2$ term first, then $x$ term, then constant.

Can I factor this expression?

You could try, but with these specific values (-1, -16, -64), the expression doesn't factor nicely into integers. The focus here is on constructing the expression correctly from given coefficients.

What if I mixed up which coefficient goes where?

Remember the pattern: a always goes with $x^2$ , b goes with $x$ , and c is the constant term (no variable). Double-check your substitution!

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Constructing an Algebraic Expression with Constants: a = -1, b = -16, c = -64

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 do all three terms have negative signs in the answer?

What if I wrote -1x² instead of -x²?

How do I know this is the standard form?

Can I factor this expression?

What if I mixed up which coefficient goes where?

🌟 Unlock Your Math Potential

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