Find the Coefficient of x² in y=-x²-3x+1: Quadratic Equation Analysis

Q: Why isn't the coefficient just 1 since there's no number in front of x²?

Great question! When you see $ -x^2 $, the coefficient is actually -1, not 1. The negative sign is part of the coefficient, and when no number appears, it's understood to be 1 (or -1 with the negative sign).

Q: How do I remember which coefficient is which?

Use the standard form $ y = ax^2 + bx + c $ as your guide:a = coefficient of $ x^2 $ termb = coefficient of $ x $ termc = constant term (no variable)

Q: What if the equation isn't written in standard form?

No problem! Just rearrange the terms to match $ y = ax^2 + bx + c $. For example, if you have $ y = 1 - 3x - x^2 $, rewrite it as $ y = -x^2 - 3x + 1 $.

Q: Can the coefficient 'a' ever be zero?

If $ a = 0 $, then you don't have an $ x^2 $ term at all! This means it's not a quadratic equation anymore - it becomes a linear equation instead.

Quadratic Coefficients with Negative Terms

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $a$ in the equation

$y=-x^2-3x+1$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's find the coefficient A. Ready? Here we go.

00:11 We'll use a special tool called the quadratic formula.

00:15 Now, we'll compare this formula to our equation to spot the coefficients.

00:20 See here, the coefficient A is attached to the X squared term. Great job!

00:35 And that's how we solve the problem. Well done!

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

$y=-x^2-3x+1$

Step-by-step solution

To determine the coefficient $a$ in the given quadratic equation $y = -x^2 - 3x + 1$ , follow these steps:

Step 1: Recognize the form of the quadratic equation as $y = ax^2 + bx + c$ .
Step 2: Identify the $x^2$ term in the equation $y = -x^2 - 3x + 1$ .
Step 3: Determine the coefficient of the $x^2$ term, which is in front of $x^2$ .

In the equation $y = -x^2 - 3x + 1$ , the term involving $x^2$ is $-x^2$ , where the coefficient $a$ is clearly $-1$ .

Hence, the value of $a$ is $a = -1$ .

Final Answer

$a=-1$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic equations follow $y = ax^2 + bx + c$ format
Technique: Identify coefficient directly in front of $x^2$ : here $-x^2$ means $a = -1$
Check: Substitute back: $y = (-1)x^2 + (-3)x + 1 = -x^2 - 3x + 1$ ✓

Common Mistakes

Avoid these frequent errors

Confusing negative signs with coefficient values
Don't think $-x^2$ means $a = 1$ = wrong coefficient! The negative sign IS part of the coefficient. Always include the sign when identifying coefficients: $-x^2$ means $a = -1$ .

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

Why isn't the coefficient just 1 since there's no number in front of x²?

Great question! When you see $-x^2$ , the coefficient is actually -1, not 1. The negative sign is part of the coefficient, and when no number appears, it's understood to be 1 (or -1 with the negative sign).

How do I remember which coefficient is which?

Use the standard form $y = ax^2 + bx + c$ as your guide:

a = coefficient of $x^2$ term
b = coefficient of $x$ term
c = constant term (no variable)

What if the equation isn't written in standard form?

No problem! Just rearrange the terms to match $y = ax^2 + bx + c$ . For example, if you have $y = 1 - 3x - x^2$ , rewrite it as $y = -x^2 - 3x + 1$ .

Can the coefficient 'a' ever be zero?

If $a = 0$ , then you don't have an $x^2$ term at all! This means it's not a quadratic equation anymore - it becomes a linear equation instead.

How can I check if I identified the coefficients correctly?

Substitute your coefficients back into the standard form! If $a = -1$ , $b = -3$ , $c = 1$ , then $y = (-1)x^2 + (-3)x + 1 = -x^2 - 3x + 1$ ✓

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