Find Coefficients in y = 3x² - 81: Quadratic Equation Analysis

Q: What does it mean when there's no x term in the equation?

When there's no x term (like in $ y = 3x^2 - 81 $), it means the coefficient b = 0. Think of it as having $ 0x $ which equals zero!

Q: Why is c = -81 and not c = 81?

The sign matters! In $ y = 3x^2 - 81 $, we're subtracting 81, so the constant term is negative 81. Always include the sign with the number.

Q: How can I remember which coefficient is which?

Use the pattern: $ ax^2 + bx + c $. The coefficient a is with $ x^2 $, b is with $ x $, and c is the number by itself (constant).

Q: Can a coefficient be zero in other positions too?

Yes! Any coefficient can be zero. For example, in $ y = 5x $, we have a = 0 and c = 0. Just remember that if a = 0, it's not really a quadratic anymore!

Quadratic Coefficients with Missing Linear Terms

Identify the coefficients based on the following equation

$y=3x^2-81$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the function coefficients

00:03 Use the formula to represent a quadratic equation

00:11 Arrange the equation to match the formula

00:31 Separate the unknown from the coefficient

00:45 Compare the formula to our equation and find the coefficients

00:51 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

Identify the coefficients based on the following equation

$y=3x^2-81$

Step-by-step solution

To solve this problem, we will identify values of $a$ , $b$ , and $c$ in the quadratic function:

Step 1: Note the given equation $y = 3x^2 - 81$ .
Step 2: Compare it to the standard quadratic form $y = ax^2 + bx + c$ .
Step 3: Match coefficients to find $a$ , $b$ , and $c$ .

Now, let's work through each step:
Step 1: The given equation is $y = 3x^2 - 81$ .
Step 2: Compare this to the standard form, $y = ax^2 + bx + c$ . In this equation:
- The coefficient of $x^2$ is 3, hence $a = 3$ .
- There is no $x$ term, which means $b = 0$ .
- The constant term is $-81$ , hence $c = -81$ .

Therefore, the solution to the problem is $a = 3, b = 0, c = -81$ .

Final Answer

$a=3,b=0,c=-81$

Key Points to Remember

Essential concepts to master this topic

Standard Form: All quadratic equations follow $y = ax^2 + bx + c$
Technique: When no x term exists, like $3x^2 - 81$ , then b = 0
Check: Rewrite as $y = 3x^2 + 0x + (-81)$ to verify coefficients ✓

Common Mistakes

Avoid these frequent errors

Confusing the constant term sign
Don't write c = 81 when the equation shows -81! This happens when students focus only on the number and ignore the negative sign. Always include the sign as part of the coefficient value.

Practice Quiz

Test your knowledge with interactive questions

What is the value of the coefficient $$ c $$ in the equation below?

$$ 4x^2+9x-2 $$

FAQ

Everything you need to know about this question

What does it mean when there's no x term in the equation?

When there's no x term (like in $y = 3x^2 - 81$ ), it means the coefficient b = 0. Think of it as having $0x$ which equals zero!

Why is c = -81 and not c = 81?

The sign matters! In $y = 3x^2 - 81$ , we're subtracting 81, so the constant term is negative 81. Always include the sign with the number.

How can I remember which coefficient is which?

Use the pattern: $ax^2 + bx + c$ . The coefficient a is with $x^2$ , b is with $x$ , and c is the number by itself (constant).

What if the equation is written differently, like 3x² - 81 = y?

Just rearrange it to standard form first! Move everything to one side so you get $y = 3x^2 - 81$ , then identify the coefficients normally.

Can a coefficient be zero in other positions too?

Yes! Any coefficient can be zero. For example, in $y = 5x$ , we have a = 0 and c = 0. Just remember that if a = 0, it's not really a quadratic anymore!

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Find Coefficients in y = 3x² - 81: Quadratic Equation Analysis

Quadratic Coefficients with Missing Linear Terms

❤️ 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 there's no x term in the equation?

Why is c = -81 and not c = 81?

How can I remember which coefficient is which?

What if the equation is written differently, like 3x² - 81 = y?

Can a coefficient be zero in other positions too?

🌟 Unlock Your Math Potential

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