Find the Coefficient of x² in y=3x-10+5x²: Identifying the Leading Term

Q: What if the equation isn't in standard form like this one?

No problem! The coefficient of $ x^2 $ stays the same regardless of order. Whether you see $ 5x^2 + 3x - 10 $ or $ 3x - 10 + 5x^2 $, the coefficient is still 5.

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

If you see just $ x^2 $ with no visible number, the coefficient is 1. Think of it as $ 1 \cdot x^2 $ - the 1 is implied but still there!

Q: Can the coefficient of x² be negative?

Absolutely! If you see $ -3x^2 $, then a = -3. The negative sign is part of the coefficient, not separate from it.

Q: How do I remember which coefficient is which?

Use the pattern: $ ax^2 + bx + c $. The letter a goes with $ x^2 $, b goes with $ x $, and c is the constant (no variable).

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

If there's no $ x^2 $ term at all, then the coefficient is 0. This means the equation is linear, not quadratic.

Quadratic Coefficients with Polynomial Identification

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $a$ in the equation

$y=3x-10+5x^2$

❤️ 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 coefficient A

00:03 We'll use the quadratic equation formula

00:09 Let's arrange the equation to fit the formula

00:14 We can see that coefficient A is for the X squared term

00:27 Let's compare the formula to our equation and find the coefficients:

00:41 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

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $a$ in the equation

$y=3x-10+5x^2$

Step-by-step solution

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

Step 1: Rewrite the given equation in standard quadratic form if necessary.
Step 2: Identify the term with $x^2$ in the equation.
Step 3: Extract the coefficient of $x^2$ as $a$ .

Now, let's work through each step:
Step 1: The provided equation is $y = 3x - 10 + 5x^2$ . Although it's not initially in standard form, observation shows that the $x^2$ term is clearly present.
Step 2: Locate the $x^2$ term: in our equation, this term is $5x^2$ .
Step 3: The coefficient of $x^2$ is $5$ . Hence, $a = 5$ .

Therefore, the coefficient of $x^2$ , or $a$ , is $a = 5$ .

Final Answer

$a=5$

Key Points to Remember

Essential concepts to master this topic

Definition: The coefficient of $x^2$ is the number multiplying the squared term
Technique: In $5x^2$ , the coefficient is 5 regardless of term order
Check: Rewrite in standard form $y = 5x^2 + 3x - 10$ to verify a = 5 ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficient with variable or constant term
Don't identify a = 3 or a = -10 just because they appear in the equation! The coefficient of $x^2$ is only the number directly multiplying the $x^2$ term. Always locate the $x^2$ term first, then identify its coefficient.

Practice Quiz

Test your knowledge with interactive questions

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $$ a $$ in the equation

$$ y=3x-10+5x^2 $$

FAQ

Everything you need to know about this question

What if the equation isn't in standard form like this one?

No problem! The coefficient of $x^2$ stays the same regardless of order. Whether you see $5x^2 + 3x - 10$ or $3x - 10 + 5x^2$ , the coefficient is still 5.

What if there's no number in front of x²?

If you see just $x^2$ with no visible number, the coefficient is 1. Think of it as $1 \cdot x^2$ - the 1 is implied but still there!

Can the coefficient of x² be negative?

Absolutely! If you see $-3x^2$ , then a = -3. The negative sign is part of the coefficient, not separate from it.

How do I remember which coefficient is which?

Use the pattern: $ax^2 + bx + c$ . The letter a goes with $x^2$ , b goes with $x$ , and c is the constant (no variable).

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

If there's no $x^2$ term at all, then the coefficient is 0. This means the equation is linear, not quadratic.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Solving Quadratic Equations 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

Find the Coefficient of x² in y=3x-10+5x²: Identifying the Leading Term

Quadratic Coefficients with Polynomial 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 the equation isn't in standard form like this one?

What if there's no number in front of x²?

Can the coefficient of x² be negative?

How do I remember which coefficient is which?

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

🌟 Unlock Your Math Potential

More Questions

The Quadratic Formula

Find the Constant Term c in y = -5x² + 4x - 3: Coefficient Analysis

Find the Coefficient of x in y=2x-3x²+1: Identifying Linear Terms

Find the Coefficient of x in y=3x²+10-x: Identifying Linear Terms

Find the Constant Term c in y = 3x² + 5: Quadratic Equation Analysis