Coefficient Identification in y=-6+x²+6x: Breaking Down Terms

Q: Why can't I just read the coefficients in the order they appear?

Because coefficients have specific positions in standard form! The coefficient a must be with $ x^2 $, b with $ x $, and c is the constant. Order matters!

Q: What if there's no visible coefficient in front of x²?

When you see just $ x^2 $ without a number, the coefficient is 1. It's like having $ 1 \cdot x^2 $ - the 1 is understood but not written.

Q: How do I handle negative signs when rearranging?

Keep the negative sign with its term! When moving $ -6 $ to the end, it becomes $ + (-6) $ or simply $ -6 $. The sign stays with the number.

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

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

Q: Can any of the coefficients be zero?

Yes! b or c can be zero, but if $ a = 0 $, it's no longer a quadratic equation. For example, $ y = x^2 - 3 $ has $ b = 0 $.

Quadratic Coefficients with Standard Form

Identify the coefficients based on the following equation

$y=-6+x^2+6x$

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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

00:10 Arrange the equation to fit the formula

00:28 Separate the variable from the coefficient

00:44 Compare the formula with our equation and find the coefficients

00:55 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

$y=-6+x^2+6x$

Step-by-step solution

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

Step 1: Identify the given equation
Step 2: Reorganize the equation to match the standard form of a quadratic equation
Step 3: Compare the terms to determine the coefficients $a$ , $b$ , and $c$

Now, let's work through each step:
Step 1: The provided equation is $y = -6 + x^2 + 6x$ .
Step 2: Rearrange the terms to match the standard form $y = ax^2 + bx + c$ . This gives us $y = x^2 + 6x - 6$ .
Step 3: Compare the terms:
The coefficient of $x^2$ (the squared term) is $a$ . Hence, $a = 1$ .
The coefficient of $x$ (the linear term) is $b$ . Hence, $b = 6$ .
The constant term is $c$ . Hence, $c = -6$ .

Therefore, the solution to the problem is that the coefficients are $a = 1, b = 6, c = -6$ .

Final Answer

$a=1,b=6,c=-6$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Rearrange to $ax^2 + bx + c$ format first
Technique: Rewrite $y = -6 + x^2 + 6x$ as $y = x^2 + 6x - 6$
Check: Verify $a = 1, b = 6, c = -6$ matches coefficient positions ✓

Common Mistakes

Avoid these frequent errors

Reading coefficients without rearranging to standard form
Don't read coefficients directly from $y = -6 + x^2 + 6x$ = wrong values like a = -6! This gives incorrect coefficient identification because terms aren't in standard order. Always rearrange to $ax^2 + bx + c$ form first.

Practice Quiz

Test your knowledge with interactive questions

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

$$ 3x^2+8x-5 $$

FAQ

Everything you need to know about this question

Why can't I just read the coefficients in the order they appear?

Because coefficients have specific positions in standard form! The coefficient a must be with $x^2$ , b with $x$ , and c is the constant. Order matters!

What if there's no visible coefficient in front of x²?

When you see just $x^2$ without a number, the coefficient is 1. It's like having $1 \cdot x^2$ - the 1 is understood but not written.

How do I handle negative signs when rearranging?

Keep the negative sign with its term! When moving $-6$ to the end, it becomes $+ (-6)$ or simply $-6$ . The sign stays with the number.

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

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

Can any of the coefficients be zero?

Yes! b or c can be zero, but if $a = 0$ , it's no longer a quadratic equation. For example, $y = x^2 - 3$ has $b = 0$ .

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Coefficient Identification in y=-6+x²+6x: Breaking Down Terms

Quadratic Coefficients with Standard Form

❤️ 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 in the order they appear?

What if there's no visible coefficient in front of x²?

How do I handle negative signs when rearranging?

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

Can any of the coefficients be zero?

🌟 Unlock Your Math Potential

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