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

Q: Why can't I just read the coefficients from left to right?

Because the equation isn't in standard form yet! The coefficients a, b, and c have specific positions: $ a $ goes with $ x^2 $, $ b $ goes with $ x $, and $ c $ is the constant term.

Q: What if there's no x term or no constant term?

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

Q: How do I handle negative signs correctly?

The sign belongs to the coefficient! In $ y = 3x^2 - x + 4 $, the coefficient of $ x $ is -1, not just 1. Always include the sign as part of the coefficient.

Q: Why is the standard form order important?

Standard form $ y = ax^2 + bx + c $ is used everywhere in mathematics! It helps with graphing, finding vertex, and using the quadratic formula. Consistent ordering prevents confusion.

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

a: Coefficient of $ x^2 $ (determines parabola direction)b: Coefficient of $ x $ (affects parabola position)c: Constant term (y-intercept value)

Quadratic Coefficients with Standard Form Arrangement

Identify the coefficients based on the following equation

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

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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 We'll use the formula for representing a quadratic equation

00:17 We'll arrange the equation to fit the formula

00:34 We'll separate the variable from the coefficient

00:50 We'll compare the formula to our equation and find the coefficients

01:00 And that's 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

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

Step-by-step solution

To solve this problem, we will match the given quadratic equation with its standard form:

Step 1: Identify the standard quadratic form as $y = ax^2 + bx + c$ .
Step 2: Compare with given equation $y = 4 + 3x^2 - x$ .
Step 3: Determine the coefficients by arranging the equation in standard form.

Let's now perform the steps:

Step 1: The standard quadratic form is $y = ax^2 + bx + c$ .

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

Step 3: Rearrange the given equation to match the standard form:

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

Now, directly compare:

$a = 3$

$b = -1$

$c = 4$

Therefore, the coefficients are correctly identified as $a=3, b=-1,$ and $c=4$ .

The correct answer is: $a=3, b=-1, c=4$ .

Final Answer

$a=3,b=-1,c=4$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic equations follow $y = ax^2 + bx + c$ pattern
Rearrangement: Rewrite $y = 4 + 3x^2 - x$ as $y = 3x^2 + (-1)x + 4$
Verification: Check coefficients match term order: a=3, b=-1, c=4 ✓

Common Mistakes

Avoid these frequent errors

Reading coefficients from original equation without rearranging
Don't read a=4, b=3, c=-1 directly from $y = 4 + 3x^2 - x$ = wrong coefficient identification! The terms aren't in standard order. Always rearrange to $y = ax^2 + bx + c$ form 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 can't I just read the coefficients from left to right?

Because the equation isn't in standard form yet! The coefficients a, b, and c have specific positions: $a$ goes with $x^2$ , $b$ goes with $x$ , and $c$ is the constant term.

What if there's no x term or no constant term?

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

How do I handle negative signs correctly?

The sign belongs to the coefficient! In $y = 3x^2 - x + 4$ , the coefficient of $x$ is -1, not just 1. Always include the sign as part of the coefficient.

Why is the standard form order important?

Standard form $y = ax^2 + bx + c$ is used everywhere in mathematics! It helps with graphing, finding vertex, and using the quadratic formula. Consistent ordering prevents confusion.

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

a: Coefficient of $x^2$ (determines parabola direction)
b: Coefficient of $x$ (affects parabola position)
c: Constant term (y-intercept value)

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

Quadratic Coefficients with Standard Form Arrangement

❤️ 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 can't I just read the coefficients from left to right?

What if there's no x term or no constant term?

How do I handle negative signs correctly?

Why is the standard form order important?

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

🌟 Unlock Your Math Potential

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