Crafting an Algebraic Expression: Using a=4, b=0, c=2

Q: What happens when one of the coefficients is zero?

When a coefficient is zero, that entire term disappears from the expression! For example, if $ b = 0 $, then $ 0x = 0 $, so we don't write it in our final answer.

Q: Do I always need to write expressions in ax² + bx + c form?

The standard form $ ax^2 + bx + c $ is helpful for identifying coefficients, but your final simplified answer should only include terms that actually exist (non-zero coefficients).

Q: What if multiple coefficients are zero?

Simply omit all terms with zero coefficients! If both a=0 and b=0, you'd just have $ c $. If only c=0, you'd have $ ax^2 + bx $.

Q: How do I know which coefficient goes with which term?

Remember the pattern: a multiplies $ x^2 $ (quadratic term)b multiplies $ x $ (linear term)c stands alone (constant term)

Q: Is 4x² + 2 still considered a quadratic expression?

Yes! Even without the linear term (bx), it's still quadratic because the highest power of x is 2. The quadratic coefficient a=4 determines this.

Quadratic Expressions with Zero Coefficients

Create an algebraic expression based on the following parameters:

$a=4,b=0,c=2$

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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

00:09 Connect the parameter to its corresponding variable according to the formula

00:26 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:

$a=4,b=0,c=2$

Step-by-step solution

To solve this problem, we need to create a quadratic expression using the given parameters.

Step 1: Identify the quadratic function format: $y = ax^2 + bx + c$ .
Step 2: Substitute the given values $a = 4$ , $b = 0$ , and $c = 2$ into the formula.
Step 3: The expression becomes $y = 4x^2 + 0x + 2$ .
Step 4: Simplify the expression by removing the term with the zero coefficient: $y = 4x^2 + 2$ .

Therefore, the solution to this problem is $4x^2 + 2$ .

Final Answer

$4x^2+2$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Use $ax^2 + bx + c$ format with given coefficients
Substitution: Replace a=4, b=0, c=2 to get $4x^2 + 0x + 2$
Simplify: Remove zero terms: $4x^2 + 0x + 2 = 4x^2 + 2$ ✓

Common Mistakes

Avoid these frequent errors

Including zero coefficient terms in final answer
Don't write $4x^2 + 0x + 2$ as your final answer = cluttered expression! Zero coefficients mean those terms don't exist in the simplified form. Always remove terms with zero coefficients to get the clean expression $4x^2 + 2$ .

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 happens when one of the coefficients is zero?

When a coefficient is zero, that entire term disappears from the expression! For example, if $b = 0$ , then $0x = 0$ , so we don't write it in our final answer.

Do I always need to write expressions in ax² + bx + c form?

The standard form $ax^2 + bx + c$ is helpful for identifying coefficients, but your final simplified answer should only include terms that actually exist (non-zero coefficients).

What if multiple coefficients are zero?

Simply omit all terms with zero coefficients! If both a=0 and b=0, you'd just have $c$ . If only c=0, you'd have $ax^2 + bx$ .

How do I know which coefficient goes with which term?

Remember the pattern:

a multiplies $x^2$ (quadratic term)
b multiplies $x$ (linear term)
c stands alone (constant term)

Is 4x² + 2 still considered a quadratic expression?

Yes! Even without the linear term (bx), it's still quadratic because the highest power of x is 2. The quadratic coefficient a=4 determines this.

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Crafting an Algebraic Expression: Using a=4, b=0, c=2

Quadratic Expressions with Zero 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 happens when one of the coefficients is zero?

Do I always need to write expressions in ax² + bx + c form?

What if multiple coefficients are zero?

How do I know which coefficient goes with which term?

Is 4x² + 2 still considered a quadratic expression?

🌟 Unlock Your Math Potential

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