Compose an Algebraic Expression: Using a=3, b=0, c=0

Q: Why do the zero terms disappear from the expression?

When you multiply any number by zero, you get zero! So $ 0 \times x = 0x = 0 $ and adding zero doesn't change the expression. We can safely remove these terms to simplify.

Q: What if only 'a' had a value and b and c were zero?

That's exactly our situation! When only the coefficient of $ x^2 $ is non-zero, you get a pure quadratic function like $ 3x^2 $ with no linear or constant terms.

Q: Is $ 3x^2 $ the same as $ x^2 \times 3 $ ?

Yes! Due to the commutative property of multiplication, $ 3x^2 = x^2 \times 3 $. However, we typically write the coefficient first by convention.

Q: How do I check if my algebraic expression is correct?

Substitute your values back into the original formula $ y = ax^2 + bx + c $. With a=3, b=0, c=0, you should get $ y = 3x^2 + 0 + 0 = 3x^2 $.

Quadratic Functions with Zero Coefficients

Create an algebraic expression based on the following parameters:

$a=3,b=0,c=0$

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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

00:08 We'll connect the parameter to the corresponding variable according to the formula

00:24 We'll write the function in its reduced form

00:32 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:

$a=3,b=0,c=0$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Substitute the given values $a = 3$ , $b = 0$ , and $c = 0$ into the quadratic function formula $y = ax^2 + bx + c$ .
Step 2: Simplify the expression.

Let's execute these steps:

Step 1: Substitute the values into the formula:
$y = 3x^2 + 0x + 0$

Step 2: Simplify the expression:
Eliminate the terms with zero coefficients to get:
$y = 3x^2$

Thus, the algebraic expression for the quadratic function with $a = 3$ , $b = 0$ , and $c = 0$ is $3x^2$ .

Therefore, the correct choice from the options provided is choice 1: $3x^2$

Final Answer

$3x^2$

Key Points to Remember

Essential concepts to master this topic

Formula: Use standard form $y = ax^2 + bx + c$ with given values
Substitution: Replace a=3, b=0, c=0 to get $y = 3x^2 + 0x + 0$
Simplify: Remove zero terms: $0x = 0$ and $+0 = 0$ to get $3x^2$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to include the coefficient with the variable
Don't write just $x^2$ when a=3 = missing the coefficient! This ignores the given parameter and creates a completely different function. Always multiply the coefficient by the variable term: $3 \times x^2 = 3x^2$ .

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 the zero terms disappear from the expression?

When you multiply any number by zero, you get zero! So $0 \times x = 0x = 0$ and adding zero doesn't change the expression. We can safely remove these terms to simplify.

What if only 'a' had a value and b and c were zero?

That's exactly our situation! When only the coefficient of $x^2$ is non-zero, you get a pure quadratic function like $3x^2$ with no linear or constant terms.

Is $3x^2$ the same as $x^2 \times 3$ ?

Yes! Due to the commutative property of multiplication, $3x^2 = x^2 \times 3$ . However, we typically write the coefficient first by convention.

How do I check if my algebraic expression is correct?

Substitute your values back into the original formula $y = ax^2 + bx + c$ . With a=3, b=0, c=0, you should get $y = 3x^2 + 0 + 0 = 3x^2$ .

What does this quadratic function look like graphically?

Since a=3 is positive and there's no linear or constant term, this creates a upward-opening parabola with its vertex at the origin (0,0). The coefficient 3 makes it steeper than $y = x^2$ .

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Compose an Algebraic Expression: Using a=3, 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 the zero terms disappear from the expression?

What if only 'a' had a value and b and c were zero?

Is $3x^2$ the same as $x^2 \times 3$ ?

How do I check if my algebraic expression is correct?

What does this quadratic function look like graphically?

🌟 Unlock Your Math Potential

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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 the zero terms disappear from the expression?

What if only 'a' had a value and b and c were zero?

Is 3x2 3x^2 3x2 the same as x2×3 x^2 \times 3 x2×3?

How do I check if my algebraic expression is correct?

What does this quadratic function look like graphically?

🌟 Unlock Your Math Potential

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