Find Coefficients in y=-4x²-3x: Quadratic Expression Analysis

Quadratic Coefficients with Missing Constant Terms

Identify the coefficients based on the following equation

y=4x23x y=-4x^2-3x

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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 to represent a quadratic equation
00:11 We'll arrange the equation to match the formula
00:25 We'll separate the variable from the coefficient
00:37 We'll compare the formula to our equation and find the coefficients
00:43 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Identify the coefficients based on the following equation

y=4x23x y=-4x^2-3x

2

Step-by-step solution

To solve this problem, we'll identify the parameters a a , b b , and c c in the quadratic function.

The quadratic equation provided is y=4x23x y = -4x^2 - 3x . To match this equation with the standard quadratic form y=ax2+bx+c y = ax^2 + bx + c , we must determine the values of a a , b b , and c c .

  • Step 1: Identify a a . The coefficient of x2 x^2 in the given equation is 4-4. Thus, a=4 a = -4 .
  • Step 2: Identify b b . The coefficient of x x in the given equation is 3-3. Thus, b=3 b = -3 .
  • Step 3: Identify c c . The constant term (the term not involving x x ) does not appear in the equation, which means c=0 c = 0 .

Therefore, the values of the parameters are a=4 a = -4 , b=3 b = -3 , and c=0 c = 0 . This matches with choice 3 in the provided options.

The correct answer is a=4,b=3,c=0 a = -4, b = -3, c = 0 .

3

Final Answer

a=4,b=3,c=0 a=-4,b=-3,c=0

Key Points to Remember

Essential concepts to master this topic
  • Standard Form: Every quadratic follows y=ax2+bx+c y = ax^2 + bx + c pattern
  • Technique: Match coefficients directly: -4 goes with x2 x^2 , -3 goes with x x
  • Check: Missing constant term means c=0 c = 0 , so a=4,b=3,c=0 a = -4, b = -3, c = 0

Common Mistakes

Avoid these frequent errors
  • Confusing coefficient positions or ignoring missing terms
    Don't mix up the order of a, b, c or forget that missing terms equal zero = wrong coefficient values! Students often think the constant term is -3 instead of recognizing it's missing. Always match each coefficient to its corresponding power of x in standard form ax2+bx+c ax^2 + bx + c .

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

What does it mean when there's no constant term in the equation?

+

When you don't see a number by itself (like +5 or -2), it means the constant term equals zero. So in y=4x23x y = -4x^2 - 3x , we have c=0 c = 0 .

How do I remember which coefficient is which?

+

Think alphabetical order! In ax2+bx+c ax^2 + bx + c : a goes with x2 x^2 , b goes with x x , and c is the constant (no x).

What if the equation is written differently like y=3x4x2 y = -3x - 4x^2 ?

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Just rearrange to standard form first! Move the x2 x^2 term to the front: y=4x23x y = -4x^2 - 3x . Then identify coefficients normally.

Can coefficients be negative numbers?

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Absolutely! Coefficients can be positive, negative, or zero. In this problem, both a and b are negative: a=4 a = -4 and b=3 b = -3 .

How can I double-check my answer?

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Substitute your coefficients back into the standard form! If a=4,b=3,c=0 a = -4, b = -3, c = 0 , then y=4x2+(3)x+0=4x23x y = -4x^2 + (-3)x + 0 = -4x^2 - 3x

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