Constructing an Algebraic Expression with a=2, b=0, c=0

Q: What if only the 'c' value was zero?

Then you'd have $ y = 2x^2 + 0x + 0 = 2x^2 $, which is still $ 2x^2 $. Only non-zero terms remain in the final expression.

Q: Is 2x² still considered a quadratic function?

Yes! As long as the highest power of x is 2 and the coefficient of $ x^2 $ is not zero, it's a quadratic function. The b and c terms are optional.

Q: How do I know which answer choice is correct?

Substitute the given parameters into $ ax^2 + bx + c $ and simplify completely. The answer that matches your simplified result is correct!

Q: What does this quadratic look like on a graph?

Since $ 2x^2 $ has no linear or constant terms, it's a parabola that opens upward with its vertex at the origin (0,0). The coefficient 2 makes it narrower than $ x^2 $.

Quadratic Functions with Zero Coefficients

Find an algebraic representation based on the parameters

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

❤️ 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

00:00 Convert the parameters to a quadratic function

00:03 We'll use the formula to represent a quadratic equation

00:11 We'll connect each parameter to its corresponding variable according to the formula

00:29 We'll write the function in its simplified form

00:33 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

Find an algebraic representation based on the parameters

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

Step-by-step solution

To solve this problem, we'll utilize the standard form of a quadratic function given by:

$y = ax^2 + bx + c$

Let's proceed with the given values for the parameters:

$a = 2$
$b = 0$
$c = 0$

Substitute these values into the quadratic function formula:

$y = 2x^2 + 0x + 0$

Simplify the expression by removing terms with zero coefficients:

$y = 2x^2$

Hence, the algebraic representation of the quadratic function with the given parameters is $2x^2$ .

After reviewing the answer choices, the correct choice is:

$2x^2$

Final Answer

$2x^2$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic functions follow $y = ax^2 + bx + c$ pattern
Substitution: Replace parameters: $y = 2x^2 + 0x + 0 = 2x^2$
Verification: Check by confirming zero terms disappear completely from expression ✓

Common Mistakes

Avoid these frequent errors

Including zero terms in final answer
Don't write $2x^2 + 0x + 0$ as your final answer = unnecessary complexity! Zero terms contribute nothing to the value and should be eliminated. Always simplify by removing terms with zero coefficients to get the cleanest form.

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

Why do we remove the 0x and +0 terms?

Zero terms don't affect the value of the expression! When you multiply zero by anything (like $0 \cdot x$ ) or add zero, the result is zero. Simplified expressions are cleaner and easier to work with.

What if only the 'c' value was zero?

Then you'd have $y = 2x^2 + 0x + 0 = 2x^2$ , which is still $2x^2$ . Only non-zero terms remain in the final expression.

Is 2x² still considered a quadratic function?

Yes! As long as the highest power of x is 2 and the coefficient of $x^2$ is not zero, it's a quadratic function. The b and c terms are optional.

How do I know which answer choice is correct?

Substitute the given parameters into $ax^2 + bx + c$ and simplify completely. The answer that matches your simplified result is correct!

What does this quadratic look like on a graph?

Since $2x^2$ has no linear or constant terms, it's a parabola that opens upward with its vertex at the origin (0,0). The coefficient 2 makes it narrower than $x^2$ .

🌟 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

Constructing an Algebraic Expression with a=2, b=0, c=0

Quadratic Functions 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

Why do we remove the 0x and +0 terms?

What if only the 'c' value was zero?

Is 2x² still considered a quadratic function?

How do I know which answer choice is correct?

What does this quadratic look like on a graph?

🌟 Unlock Your Math Potential

More Questions

Standard Representation

Construct an Algebraic Expression Using a=1, b=1, c=0

Create an Algebraic Expression with Variables a=4, b=-2, c=16

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

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

Plotting Functions with Parameters

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

Craft an Algebraic Expression Using Parameters: a = -1, b = 1, c = 2

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

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

The function y=ax²+bx+c

Create an Algebraic Expression with Given Parameters: a=4, b=2, c=5

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

Create an Algebraic Expression Using a = 1/2, b = 1/2, c = 1/2

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