Identify Coefficients in y=3x²+3x-4: Quadratic Expression Analysis

Q: What if there's no x² term in the equation?

If there's no $ x^2 $ term, then a = 0 and the equation is linear, not quadratic. A true quadratic must have $ a ≠ 0 $.

Q: How do I remember which coefficient is which?

Use the pattern ABC: a goes with x², b goes with x¹, and c is the constant (x⁰). Think alphabetical order matching decreasing powers!

Q: What if the equation isn't written in standard form?

Always rearrange first! Move all terms to one side so you have $ ax^2 + bx + c = 0 $ or $ y = ax^2 + bx + c $ before identifying coefficients.

Q: Can coefficients be negative or zero?

Absolutely! Coefficients can be any real number including negative, positive, zero, or fractions. Just remember that for a quadratic, a cannot be zero.

Quadratic Coefficients with Standard Form Identification

Identify the coefficients based on the following equation

$y=3x^2+3x-4$

❤️ 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

00:00 Find the function coefficients

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

00:13 We'll separate the variable from the coefficient

00:32 We'll compare the formula to our equation and find the coefficients:

00:40 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

$y=3x^2+3x-4$

Step-by-step solution

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

Step 1: Compare the given quadratic function with the standard form.
Step 2: Directly identify the coefficients $a$ , $b$ , and $c$ .
Step 3: Verify the correct choice from the provided options, if applicable.

Now, let's work through each step:
Step 1: The given quadratic function is $y = 3x^2 + 3x - 4$ . The standard form for a quadratic equation is $y = ax^2 + bx + c$ .
Step 2: By comparing the given equation to the standard form, we can identify the coefficients:
- $a = 3$ , from the term $3x^2$ .
- $b = 3$ , from the term $3x$ .
- $c = -4$ , from the constant term $-4$ .
Step 3: With these values, compare them to the given choices. The choice that matches these values is option 3: $a = 3, b = 3, c = -4$ .

Therefore, the solution to the problem is $a = 3, b = 3, c = -4$ .

Final Answer

$a=3,b=3,c=-4$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Always use $y = ax^2 + bx + c$ as reference
Technique: Match terms directly: $3x^2$ gives $a = 3$ , $3x$ gives $b = 3$
Check: Substitute back: $3x^2 + 3x + (-4) = 3x^2 + 3x - 4$ ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficient positions or signs
Don't mix up the order of coefficients like writing a = -4, b = 3, c = 3 = completely wrong identification! The coefficient positions must match their corresponding terms exactly. Always identify a from the x² term, b from the x term, and c from the constant term in that specific order.

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 if there's no x² term in the equation?

If there's no $x^2$ term, then a = 0 and the equation is linear, not quadratic. A true quadratic must have $a ≠ 0$ .

What happens if a coefficient is missing, like just x instead of 3x?

When you see just x without a number, the coefficient is 1. Similarly, -x has a coefficient of -1.

How do I remember which coefficient is which?

Use the pattern ABC: a goes with x², b goes with x¹, and c is the constant (x⁰). Think alphabetical order matching decreasing powers!

What if the equation isn't written in standard form?

Always rearrange first! Move all terms to one side so you have $ax^2 + bx + c = 0$ or $y = ax^2 + bx + c$ before identifying coefficients.

Can coefficients be negative or zero?

Absolutely! Coefficients can be any real number including negative, positive, zero, or fractions. Just remember that for a quadratic, a cannot be zero.

🌟 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

Identify Coefficients in y=3x²+3x-4: Quadratic Expression Analysis

Quadratic Coefficients with Standard Form Identification

❤️ 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 if there's no x² term in the equation?

What happens if a coefficient is missing, like just x instead of 3x?

How do I remember which coefficient is which?

What if the equation isn't written in standard form?

Can coefficients be negative or zero?

🌟 Unlock Your Math Potential

More Questions

Plotting Functions with Parameters

Find Coefficients in y = 6x - 6x² + 3: Identifying a, b, and c

Identify Coefficients in y = -4x² + 3: Quadratic Equation Analysis

Identify Coefficients in y=5x+3x²: Term-by-Term Analysis

Identify Coefficients in y=-x² + x + 5: Quadratic Equation Analysis

The function y=ax²+bx+c

Identify Coefficients in the Equation 6=6x+2x²: Term Analysis

Identify Coefficients in y=-3x²-4: Quadratic Function Analysis

Solve y=x²+x+5: Understanding Quadratic Functions in Standard Form