Create an Algebraic Expression with Parameters: a=2, b=0, c=6

Q: What does the standard form ax² + bx + c actually mean?

The standard form is like a template for quadratic expressions. The letter a is always the coefficient of x², b is the coefficient of x, and c is the constant term that stands alone.

Q: Why does 0x disappear from the expression?

When you multiply any number by zero, you get zero! Since $ 0x = 0 $ for any value of x, adding zero doesn't change the expression, so we can omit it completely.

Q: How do I remember which parameter goes where?

Think alphabetically: a comes first (with x²), b comes second (with x), and c comes last (by itself). Or remember: biggest power first - x² has the highest power, so its coefficient comes first.

Q: Can I write the answer in a different order?

While $ 6 + 2x^2 $ equals $ 2x^2 + 6 $, standard form means writing terms in descending order by power: x² term first, then x term, then constant.

Quadratic Expressions with Given Coefficients

Create an algebraic expression based on the following parameters:

$a=2,b=0,c=6$

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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 Connect the parameter to its corresponding variable according to the formula

00:33 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:

$a=2,b=0,c=6$

Step-by-step solution

To solve this problem, we will construct an algebraic expression using the given parameters in a quadratic function format.

Step 1: Identify the formula required. The standard quadratic function is given by $ax^2 + bx + c$ .
Step 2: Substitute the given values of $a$ , $b$ , and $c$ . We have $a = 2$ , $b = 0$ , and $c = 6$ .
Step 3: Insert these values into the formula: $2x^2 + 0x + 6$ .
Step 4: Simplify the expression. Since the coefficient of $x$ is zero, $0x$ can be omitted. This simplifies the expression to $2x^2 + 6$ .

The final algebraic expression, representing the given parameters in a quadratic form, is $2x^2 + 6$ .

Therefore, the correct algebraic expression is $2x^2 + 6$ .

Final Answer

$2x^2+6$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Use $ax^2 + bx + c$ with given parameter values
Substitution: Replace a=2, b=0, c=6 to get $2x^2 + 0x + 6$
Simplification: Remove zero terms: $0x$ disappears, leaving $2x^2 + 6$ ✓

Common Mistakes

Avoid these frequent errors

Mixing up parameter positions in standard form
Don't put c=6 in front of x² and a=2 as the constant = $6x^2 + 2$ ! This switches the quadratic and constant terms. Always remember: a goes with x², b goes with x, and c is the constant term.

Practice Quiz

Test your knowledge with interactive questions

What is the value of the coefficient $$ c $$ in the equation below?

$$ 4x^2+9x-2 $$

FAQ

Everything you need to know about this question

What does the standard form ax² + bx + c actually mean?

The standard form is like a template for quadratic expressions. The letter a is always the coefficient of x², b is the coefficient of x, and c is the constant term that stands alone.

Why does 0x disappear from the expression?

When you multiply any number by zero, you get zero! Since $0x = 0$ for any value of x, adding zero doesn't change the expression, so we can omit it completely.

What if b was a different number, not zero?

If b ≠ 0, you'd keep the middle term! For example, if b = 3, your expression would be $2x^2 + 3x + 6$ . The middle term only disappears when its coefficient is zero.

How do I remember which parameter goes where?

Think alphabetically: a comes first (with x²), b comes second (with x), and c comes last (by itself). Or remember: biggest power first - x² has the highest power, so its coefficient comes first.

Can I write the answer in a different order?

While $6 + 2x^2$ equals $2x^2 + 6$ , standard form means writing terms in descending order by power: x² term first, then x term, then constant.

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Create an Algebraic Expression with Parameters: a=2, b=0, c=6

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 the standard form ax² + bx + c actually mean?

Why does 0x disappear from the expression?

What if b was a different number, not zero?

How do I remember which parameter goes where?

Can I write the answer in a different order?

🌟 Unlock Your Math Potential

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