Crafting an Algebraic Expression with a=3, b=0, and c=1/3

Q: What happens when b = 0 in a quadratic expression?

When b = 0, the middle term $ bx $ becomes $ 0x = 0 $, so it disappears! Your expression becomes just $ ax^2 + c $.

Q: Do I always write the expression as ax² + bx + c?

Start with the standard form $ ax^2 + bx + c $ to organize your substitution, then simplify by removing any zero terms to get your final answer.

Q: Why is the constant term 1/3 and not just 1?

The problem specifically gives $ c = \frac{1}{3} $. Always use the exact values provided in the problem - don't change fractions to whole numbers!

Q: Could the answer be negative if the coefficients were different?

Absolutely! If $ a $ were negative (like a = -3), you'd get $ -3x^2 + \frac{1}{3} $. Always use the signs of the given coefficients.

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

Verify each coefficient matches: the number in front of $ x^2 $ should be 3, there should be no $ x $ term, and the constant should be $ \frac{1}{3} $.

Quadratic Functions with Coefficient Substitution

Create an algebraic expression based on the following parameters:

$a=3,b=0,c=\frac{1}{3}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's start by changing the parameters into a quadratic function.

00:13 We're going to use the quadratic formula. It helps us represent a quadratic equation.

00:25 Now, match each parameter with the corresponding variable in the formula.

00:44 Next, simplify the function into its reduced form.

01:02 And there you have it! That's how we solve this problem.

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:

$a=3,b=0,c=\frac{1}{3}$

Step-by-step solution

To solve the problem, we need to substitute the given coefficients into the standard form of a quadratic function.

Step 1: Identify the coefficients from the problem parameters: $a = 3$ , $b = 0$ , $c = \frac{1}{3}$ .
Step 2: Substitute these values into the quadratic expression $ax^2 + bx + c$ . This gives us $3x^2 + 0 \cdot x + \frac{1}{3}$ .
Step 3: Simplify the expression by removing the term with $0 \cdot x$ , resulting in $3x^2 + \frac{1}{3}$ .

Thus, the algebraic expression for the given parameters is $3x^2 + \frac{1}{3}$ .

Final Answer

$3x^2+\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic expressions follow the pattern ax² + bx + c
Substitution: Replace a=3, b=0, c=1/3 to get $3x^2 + 0x + \frac{1}{3}$
Simplify: Remove zero terms: $0x = 0$ disappears, leaving $3x^2 + \frac{1}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to include the constant term or mixing up coefficient positions
Don't write 3x² + 0 or put coefficients in wrong positions = missing parts of the expression! This ignores given values and creates incomplete expressions. Always substitute each coefficient (a, b, c) into its correct position in ax² + bx + c, then simplify.

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 happens when b = 0 in a quadratic expression?

When b = 0, the middle term $bx$ becomes $0x = 0$ , so it disappears! Your expression becomes just $ax^2 + c$ .

Do I always write the expression as ax² + bx + c?

Start with the standard form $ax^2 + bx + c$ to organize your substitution, then simplify by removing any zero terms to get your final answer.

Why is the constant term 1/3 and not just 1?

The problem specifically gives $c = \frac{1}{3}$ . Always use the exact values provided in the problem - don't change fractions to whole numbers!

Could the answer be negative if the coefficients were different?

Absolutely! If $a$ were negative (like a = -3), you'd get $-3x^2 + \frac{1}{3}$ . Always use the signs of the given coefficients.

How do I check if my expression is correct?

Verify each coefficient matches: the number in front of $x^2$ should be 3, there should be no $x$ term, and the constant should be $\frac{1}{3}$ .

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Crafting an Algebraic Expression with a=3, b=0, and c=1/3

Quadratic Functions with Coefficient Substitution

❤️ 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 b = 0 in a quadratic expression?

Do I always write the expression as ax² + bx + c?

Why is the constant term 1/3 and not just 1?

Could the answer be negative if the coefficients were different?

How do I check if my expression is correct?

🌟 Unlock Your Math Potential

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