Create an Algebraic Expression Using Constants a=1, b=16, c=64

Q: What if the coefficient a equals 1? Do I still write it?

When a = 1, you can write either $ 1x^2 $ or simply $ x^2 $. Both are correct, but $ x^2 $ is the simplified form most commonly used.

Q: How do I remember which coefficient goes where?

Use the phrase "A-B-C order": coefficient A goes with x², coefficient B goes with x, and coefficient C stands alone as the constant term.

Q: Can I rearrange the terms in a different order?

While mathematically equivalent, standard form always writes terms in descending order of powers: $ x^2 $ first, then $ x $, then the constant.

Q: How do I know if my final expression is correct?

Check three things: Coefficient of $ x^2 $ matches your a valueCoefficient of $ x $ matches your b valueConstant term matches your c value

Quadratic Expressions with Given 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

00:13 Connect the parameter to the corresponding unknown according to the formula

00:30 Write the function in its reduced form

00:37 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 this problem, let's proceed with the construction of the quadratic expression:

Step 1: Recognize the standard form of a quadratic expression, which is $ax^2 + bx + c$ .
Step 2: Substitute the given values into this formula:
- $a = 1$
- $b = 16$
- $c = 64$
Plugging in these values, we determine the expression to be $1x^2 + 16x + 64$ , which simplifies to $x^2 + 16x + 64$ .

Thus, the algebraic expression we derive from these parameters is the quadratic expression:

$x^2 + 16x + 64$

This matches the correct choice provided in the given multiple-choice options.

Final Answer

$x^2+16x+64$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic expressions follow $ax^2 + bx + c$
Substitution: Replace a=1, b=16, c=64 to get $x^2 + 16x + 64$
Verification: Check coefficient order matches a, b, c exactly ✓

Common Mistakes

Avoid these frequent errors

Mixing up coefficient positions in standard form
Don't place coefficients randomly like c=64 with x² term = $64x^2 + 16x + 1$ ! This ignores the standard quadratic form completely. Always place coefficients in order: a with x², b with x, and c as the constant term.

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

What if the coefficient a equals 1? Do I still write it?

When a = 1, you can write either $1x^2$ or simply $x^2$ . Both are correct, but $x^2$ is the simplified form most commonly used.

How do I remember which coefficient goes where?

Use the phrase "A-B-C order": coefficient A goes with x², coefficient B goes with x, and coefficient C stands alone as the constant term.

What if one of the coefficients is negative?

Just substitute the negative value directly! If b = -16, your expression becomes $x^2 - 16x + 64$ . The sign is part of the coefficient.

Can I rearrange the terms in a different order?

While mathematically equivalent, standard form always writes terms in descending order of powers: $x^2$ first, then $x$ , then the constant.

How do I know if my final expression is correct?

Check three things:

Coefficient of $x^2$ matches your a value
Coefficient of $x$ matches your b value
Constant term matches your c value

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Create an Algebraic Expression Using Constants a=1, b=16, c=64

Quadratic Expressions with Given 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

What if the coefficient a equals 1? Do I still write it?

How do I remember which coefficient goes where?

What if one of the coefficients is negative?

Can I rearrange the terms in a different order?

How do I know if my final expression is correct?

🌟 Unlock Your Math Potential

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