Create an Algebraic Expression with a=2, b=0, c=4

Q: What does it mean when b=0 in a quadratic expression?

When b=0, it means there's no linear term (no x term). The expression becomes just $ ax^2 + c $, which creates a symmetric parabola centered on the y-axis.

Q: Do I still write the bx term even if b=0?

Initially, yes! Write $ 2x^2 + 0x + 4 $ to show your substitution work. Then simplify by removing the zero term to get $ 2x^2 + 4 $.

Q: How do I know which expression form to use?

The problem asks you to create an expression with given coefficients a, b, and c. This tells you to use the standard quadratic form $ ax^2 + bx + c $ and substitute the values.

Q: What if a or c were zero instead of b?

If a=0, you'd get a linear expression like $ bx + c $. If c=0, you'd get $ ax^2 + bx $. Always substitute first, then simplify!

Q: Is my final answer supposed to have an equals sign?

No! The question asks for an algebraic expression, not an equation. Your answer should be just $ 2x^2 + 4 $ without any equals sign.

Quadratic Expressions with Zero Linear Term

Create an algebraic expression based on the following parameters:

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

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's convert the parameters into a quadratic function.

00:13 We'll use a formula to create the quadratic equation. Are you ready?

00:21 Now, connect each parameter to its matching variable based on the formula. Take your time.

00:40 Next, we'll write the function in its simplest form. Almost there!

00:47 And that's how we find the solution to our question. Well done!

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:

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

Step-by-step solution

To solve this problem, we will derive the algebraic expression step-by-step:

Step 1: Identify the given information:
The problem states $a = 2$ , $b = 0$ , and $c = 4$ .

Step 2: Write the standard quadratic expression:
The general form is $y = ax^2 + bx + c$ .

Step 3: Substitute the given values into the expression:
Replace $a$ with 2, $b$ with 0, and $c$ with 4:
$y = 2x^2 + 0x + 4$ .

Step 4: Simplify the expression:
Since $0x$ is zero, the expression simplifies to:
$y = 2x^2 + 4$ .

Thus, the algebraic expression based on the given parameters is $2x^2 + 4$ .

The correct answer is: $2x^2 + 4$ (Choice 1).

Final Answer

$2x^2+4$

Key Points to Remember

Essential concepts to master this topic

Standard Form: The general quadratic form is $ax^2 + bx + c$
Substitution: Replace a=2, b=0, c=4 to get $2x^2 + 0x + 4$
Simplification: Since $0x = 0$ , the final expression is $2x^2 + 4$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to include the constant term when b=0
Don't write just $2x^2$ when b=0 = missing the constant! This ignores the c value completely. Always include all three terms initially: $ax^2 + bx + c$ , then simplify by removing zero terms.

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 does it mean when b=0 in a quadratic expression?

When b=0, it means there's no linear term (no x term). The expression becomes just $ax^2 + c$ , which creates a symmetric parabola centered on the y-axis.

Do I still write the bx term even if b=0?

Initially, yes! Write $2x^2 + 0x + 4$ to show your substitution work. Then simplify by removing the zero term to get $2x^2 + 4$ .

How do I know which expression form to use?

The problem asks you to create an expression with given coefficients a, b, and c. This tells you to use the standard quadratic form $ax^2 + bx + c$ and substitute the values.

What if a or c were zero instead of b?

If a=0, you'd get a linear expression like $bx + c$ . If c=0, you'd get $ax^2 + bx$ . Always substitute first, then simplify!

Is my final answer supposed to have an equals sign?

No! The question asks for an algebraic expression, not an equation. Your answer should be just $2x^2 + 4$ without any equals sign.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 The Quadratic Function questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Create an Algebraic Expression with a=2, b=0, c=4

Quadratic Expressions with Zero Linear Term

❤️ 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 it mean when b=0 in a quadratic expression?

Do I still write the bx term even if b=0?

How do I know which expression form to use?

What if a or c were zero instead of b?

Is my final answer supposed to have an equals sign?

🌟 Unlock Your Math Potential

More Questions

Standard Representation

Building an Algebraic Expression Using Values a = -1, b = -6, c = 9

Craft an Algebraic Expression with Given Constants: a=5, b=3, c=-4

Specific Algebra Task: Create an Expression with a = -3, b = 15, c = 0

Constructing an Algebraic Expression: Using a = 4, b = 2, c = 1/2

The function y=ax²+bx+c

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

Evaluate Algebraic Expressions with Given Parameters: a = -3, b = 3, c = 7

Developing an Algebraic Expression: Substitute Values a=-10, b=2, c=0

The Algebraic Expression Challenge: Formulate Using a=3, b=6, c=9

Plotting Functions with Parameters

Formulate an Algebraic Expression: Use Parameters a=1, b=-1, c=3

Create an Algebraic Expression: Using Parameters a=1, b=2, c=0

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

Constructing an Algebraic Expression: Parameters a = -1, b = 0, c = 0 Explained