Identify Coefficients in the Quadratic Function y=x²

Quadratic Functions with Standard Form Coefficients

Identify the coefficients based on the following equation

y=x2 y=x^2

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the function's coefficients
00:03 Use the formula to represent a quadratic equation
00:19 Arrange the equation to match the formula
00:39 Separate the unknown from the coefficient
00:53 Compare the formula to our equation and find the coefficients
01:01 And this is the solution to the question

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=x2 y=x^2

2

Step-by-step solution

To solve this problem, let's follow these steps:

  • Step 1: Recognize the standard form of a quadratic equation.
  • Step 2: Match the given function to the standard form.
  • Step 3: Identify each coefficient a a , b b , and c c .

Now, let's work through these steps:

Step 1: The standard form of a quadratic function is y=ax2+bx+c y = ax^2 + bx + c . Our goal is to identify a a , b b , and c c .

Step 2: We are given the function y=x2 y = x^2 . This can be aligned with the standard form as y=1x2+0x+0 y = 1 \cdot x^2 + 0 \cdot x + 0 .

Step 3: By comparing the given function y=x2 y = x^2 with the standard form, we can deduce:
- The coefficient of x2 x^2 is 1, so a=1 a = 1 .
- The linear term coefficient is missing, which implies b=0 b = 0 .
- There is no constant term, so c=0 c = 0 .

Therefore, the coefficients are a=1,b=0,c=0 a = 1, b = 0, c = 0 , corresponding to choice 1.

3

Final Answer

a=1,b=0,c=0 a=1,b=0,c=0

Key Points to Remember

Essential concepts to master this topic
  • Standard Form: Any quadratic function follows y=ax2+bx+c y = ax^2 + bx + c
  • Technique: Rewrite y=x2 y = x^2 as y=1x2+0x+0 y = 1x^2 + 0x + 0
  • Check: Verify coefficients match: a=1,b=0,c=0 a = 1, b = 0, c = 0

Common Mistakes

Avoid these frequent errors
  • Assuming missing terms have coefficient 1
    Don't think that missing x term means b = 1 or missing constant means c = 1! Missing terms actually have coefficient 0, not 1. Always remember that no term visible means coefficient equals zero.

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 is the coefficient of x² equal to 1 when I don't see a 1?

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When no number appears before x2 x^2 , there's an invisible 1! Just like how x means 1x, the expression x2 x^2 means 1x2 1x^2 .

What happens to terms that aren't written in the equation?

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Missing terms have a coefficient of 0, not 1! In y=x2 y = x^2 , there's no x term and no constant, so b=0 b = 0 and c=0 c = 0 .

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).

Can coefficients be negative or zero?

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Absolutely! Coefficients can be any real number. However, for a function to be quadratic, a cannot equal 0 (otherwise it wouldn't have an x2 x^2 term).

Is there a quick way to identify coefficients?

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Yes!

  • Find the number in front of x2 x^2 → that's a
  • Find the number in front of x x → that's b
  • Find the number by itself → that's c

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