Find the Coefficient: What is 'c' in 4x^2 + 9x - 2?

Quadratic Coefficients with Standard Form Identification

What is the value of the coefficient c c in the equation below?

4x2+9x2 4x^2+9x-2

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Step-by-step video solution

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00:00 Find the value of coefficient C in the equation
00:04 Let's look at the coefficients of the quadratic equation
00:11 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

What is the value of the coefficient c c in the equation below?

4x2+9x2 4x^2+9x-2

2

Step-by-step solution

The quadratic equation is given as 4x2+9x2 4x^2 + 9x - 2 . This equation is in the standard form of a quadratic equation, which is ax2+bx+c ax^2 + bx + c , where a a , b b , and c c are coefficients.

  • The term 4x2 4x^2 indicates that the coefficient a=4 a = 4 .
  • The term 9x 9x indicates that the coefficient b=9 b = 9 .
  • The constant term 2-2 indicates that the coefficient c=2 c = -2 .

From this analysis, we can see that the coefficient c c is 2-2.

Therefore, the value of the coefficient c c in the equation is 2-2.

3

Final Answer

-2

Key Points to Remember

Essential concepts to master this topic
  • Standard Form: Quadratic equations follow ax2+bx+c ax^2 + bx + c pattern
  • Position Method: Find c by identifying the constant term: -2
  • Verification: Check all coefficients match: a=4, b=9, c=-2 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing coefficient positions in standard form
    Don't assume c is always the first number you see = wrong coefficient identification! Students often pick 4 or 9 instead of recognizing position matters. Always identify c as the constant term with no variable attached.

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

What exactly is the 'c' coefficient in a quadratic?

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The c coefficient is the constant term in standard form ax2+bx+c ax^2 + bx + c . It's the number with no variable attached to it. In 4x2+9x2 4x^2 + 9x - 2 , that's -2.

Why isn't 4 the answer since it's the first number?

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Position in the equation doesn't determine the coefficient name! The coefficient names (a, b, c) are based on which term they belong to, not their order. The 4 is coefficient 'a' because it's with x2 x^2 .

What if the equation was written in a different order?

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The coefficients stay the same! Whether you write 4x2+9x2 4x^2 + 9x - 2 or 2+9x+4x2 -2 + 9x + 4x^2 , the c coefficient is still -2 because it's the constant term.

How do I remember which coefficient is which?

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Think alphabetically! a goes with x2 x^2 (highest power), b goes with x x (middle power), and c is the constant (no variable power).

What if there's no constant term visible?

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If you don't see a constant term, then c = 0! For example, in 3x2+5x 3x^2 + 5x , we can write it as 3x2+5x+0 3x^2 + 5x + 0 , so c = 0.

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