Find Coefficients in y=3+3x²-4x: Term-by-Term Analysis

Q: Why do I need to rearrange the equation first?

The standard form $ ax^2 + bx + c $ has a specific order: highest degree first, then lower degrees. Without rearranging, you might assign coefficients to the wrong variables!

Q: How do I handle negative signs correctly?

The sign is part of the coefficient! In $ -4x $, the coefficient is $ -4 $, not $ 4 $. Always include the sign when identifying coefficients.

Q: What's the difference between a, b, and c?

a: coefficient of $ x^2 $ term (quadratic coefficient)b: coefficient of $ x $ term (linear coefficient)c: constant term (no variable)

Q: Can I solve this without writing it in standard form?

While possible, it's much easier to make mistakes that way. Standard form ensures you match each coefficient to the correct variable power every time!

Quadratic Coefficients with Standard Form Rearrangement

Identify the coefficients based on the following equation

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find the coefficients of the function.

00:09 To do this, we use the formula for a quadratic equation.

00:15 First, arrange the equation so it looks just like the quadratic formula.

00:34 Next, separate the variable from its coefficient. Take your time.

00:48 Then, compare the formula to your equation and find those coefficients.

00:54 Great job! That's the solution to our 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

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

Step-by-step solution

Let's solve the problem step-by-step:

Our task is to identify the coefficients $a$ , $b$ , and $c$ in the quadratic function, which is written in the form $y = ax^2 + bx + c$ .

The given equation is $y = 3 + 3x^2 - 4x$ .

Step 1: Rewrite the equation in the standard quadratic form $ax^2 + bx + c$ . It becomes $y = 3x^2 - 4x + 3$ .
Step 2: Compare term by term with $ax^2 + bx + c$ :

Upon comparison, we find:

The coefficient of $x^2$ is $a = 3$ .
The coefficient of $x$ is $b = -4$ .
The constant term is $c = 3$ .

Therefore, the parameters are:

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

The correct answer among the choices is choice 2: $a=3,b=-4,c=3$ .

Final Answer

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

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic equations must be written as $ax^2 + bx + c$
Technique: Rearrange $3 + 3x^2 - 4x$ to $3x^2 - 4x + 3$
Check: Verify $a = 3$ , $b = -4$ , $c = 3$ by comparing with standard form ✓

Common Mistakes

Avoid these frequent errors

Reading coefficients from equation without rearranging
Don't read coefficients directly from $y = 3 + 3x^2 - 4x$ = wrong order! This gives coefficients in wrong positions like a=3, b=3, c=-4. Always rearrange to standard form $ax^2 + bx + c$ first.

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

Why do I need to rearrange the equation first?

The standard form $ax^2 + bx + c$ has a specific order: highest degree first, then lower degrees. Without rearranging, you might assign coefficients to the wrong variables!

What if there's no x term in the equation?

If a term is missing, its coefficient is 0. For example, in $y = 2x^2 + 5$ , there's no x term, so $b = 0$ .

How do I handle negative signs correctly?

The sign is part of the coefficient! In $-4x$ , the coefficient is $-4$ , not $4$ . Always include the sign when identifying coefficients.

What's the difference between a, b, and c?

a: coefficient of $x^2$ term (quadratic coefficient)
b: coefficient of $x$ term (linear coefficient)
c: constant term (no variable)

Can I solve this without writing it in standard form?

While possible, it's much easier to make mistakes that way. Standard form ensures you match each coefficient to the correct variable power every time!

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Find Coefficients in y=3+3x²-4x: Term-by-Term Analysis

Quadratic Coefficients with Standard Form Rearrangement

❤️ 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 I need to rearrange the equation first?

What if there's no x term in the equation?

How do I handle negative signs correctly?

What's the difference between a, b, and c?

Can I solve this without writing it in standard form?

🌟 Unlock Your Math Potential

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