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

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

No problem! You can identify coefficients from any order. Just look for the number in front of each term: x² term, x term, and constant term.

Q: Can coefficients be negative?

Absolutely! Coefficients can be positive, negative, or even fractions. Just make sure to include the sign when identifying them.

Q: What if there's no x term visible?

If you don't see an x term (like in $ y = x^2 + 5 $), then b = 0. The coefficient is 0 when a term is missing.

Quadratic Coefficients with Standard Form Recognition

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $b$ in the equation

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find coefficient B

00:03 We'll use the quadratic equation formula

00:12 We'll arrange the equation to match the formula

00:20 We'll compare the formula to our equation and find the coefficients

00:29 We can see that coefficient B belongs to the X term

00:37 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 $b$ in the equation

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

Step-by-step solution

To solve this problem, we need to identify the coefficients in the given quadratic equation:

The equation provided is $y = 2x - 3x^2 + 1$ .
The standard form of a quadratic equation is $ax^2 + bx + c$ .
From the equation, identify:
- The $ax^2$ term is $-3x^2$ , indicating $a = -3$ .
- The $bx$ term is $2x$ , indicating $b = 2$ .
- The constant term $c$ is $1$ .

Thus, the coefficient $b$ in the equation $y = 2x - 3x^2 + 1$ is $b = 2$ , which corresponds to choice 1.

Final Answer

$b=2$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Arrange quadratic equations as $ax^2 + bx + c$
Technique: Identify coefficient of x term: in 2x - 3x² + 1, b = 2
Check: Verify by matching each term to standard form positions ✓

Common Mistakes

Avoid these frequent errors

Confusing x² and x coefficients
Don't mix up a and b values when terms aren't in standard order = wrong coefficient identification! Students often pick -3 because it looks prominent. Always identify which variable each coefficient belongs to first.

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 answer -3 if it's the biggest number?

The coefficient b specifically refers to the number in front of the x term, not x². In $2x - 3x^2 + 1$ , -3 is the coefficient of x², while 2 is the coefficient of x.

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

No problem! You can identify coefficients from any order. Just look for the number in front of each term: x² term, x term, and constant term.

Can coefficients be negative?

Absolutely! Coefficients can be positive, negative, or even fractions. Just make sure to include the sign when identifying them.

What if there's no x term visible?

If you don't see an x term (like in $y = x^2 + 5$ ), then b = 0. The coefficient is 0 when a term is missing.

How do I remember which coefficient is which?

Think alphabetically: a comes first so it goes with x² (highest power), b comes next so it goes with x, and c is the constant (no variable).

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