Create an Algebraic Expression Using the Given Parameters: a = 2, b = 4, c = 8

Q: What does 'standard form' mean for quadratic expressions?

Standard form is $ ax^2 + bx + c $ where terms are arranged in descending order of powers. The highest power ($ x^2 $) comes first, then x, then the constant.

Quadratic Expressions with Given Coefficients

Create an algebraic expression based on the following parameters:

$a=2,b=4,c=8$

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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 Use the formula to represent a quadratic equation

00:08 Connect the parameter to the corresponding variable according to the formula

00:30 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:

$a=2,b=4,c=8$

Step-by-step solution

To solve this problem, we need to form an algebraic expression for a quadratic function using given parameters.

We start by recalling the standard form of a quadratic function: $( ax^2 + bx + c )$ . In this expression:

$a$ is the coefficient of $x^2$
$b$ is the coefficient of $x$
$c$ is the constant term

Given the values are $a = 2$ , $b = 4$ , and $c = 8$ , we substitute these into the standard form equation:

$ax^2 + bx + c = 2x^2 + 4x + 8$

This yields the algebraic expression for the quadratic function.

The correct expression, given all calculations and simplifications, is $2x^2 + 4x + 8$ .

Referring to the choices provided, the correct choice is:

: $( 2x^2 + 4x + 8 )$

Therefore, the solution to the problem is $\boxed{2x^2 + 4x + 8}$ .

Final Answer

$2x^2+4x+8$

Key Points to Remember

Essential concepts to master this topic

Standard Form: $ax^2 + bx + c$ where a, b, c are coefficients
Substitution: Replace each letter with its value: a=2, b=4, c=8
Verification: Check final expression $2x^2 + 4x + 8$ matches all given values ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficient positions in quadratic form
Don't place coefficients in wrong positions like $8x^2 + 2x + 4$ = incorrect expression! This happens when you mix up which parameter goes with which term. Always remember the order: a goes with $x^2$ , b goes with x, and c is the constant.

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 'standard form' mean for quadratic expressions?

Standard form is $ax^2 + bx + c$ where terms are arranged in descending order of powers. The highest power ( $x^2$ ) comes first, then x, then the constant.

Do I always need to include all three terms?

Yes! Even if a coefficient is given, you must include its corresponding term. In this problem, since a=2, b=4, and c=8 are all given, your expression needs all three terms: $2x^2 + 4x + 8$ .

What if one of the coefficients was zero?

If a coefficient is zero, that term disappears from the expression. For example, if b=0, you'd get $ax^2 + c$ . But in this problem, all coefficients are non-zero.

Can I rearrange the terms in a different order?

While mathematically equivalent, always write quadratic expressions in standard form with decreasing powers: $x^2$ term first, then x term, then constant.

How do I know which answer choice is correct?

Match each coefficient in your expression to the given values. The correct answer $2x^2 + 4x + 8$ has: coefficient of $x^2$ is 2 ✓, coefficient of x is 4 ✓, constant is 8 ✓.

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Create an Algebraic Expression Using the Given Parameters: a = 2, b = 4, c = 8

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 does 'standard form' mean for quadratic expressions?

Do I always need to include all three terms?

What if one of the coefficients was zero?

Can I rearrange the terms in a different order?

How do I know which answer choice is correct?

🌟 Unlock Your Math Potential

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