Find Coefficients in the Quadratic Equation: y = x² - 6x + 4

Q: Why is the coefficient of x equal to -6 and not +6?

In $ y = x^2 - 6x + 4 $, we can rewrite this as $ y = x^2 + (-6)x + 4 $. The coefficient is the number multiplying the variable, including its sign. So b = -6.

Q: What if there's no number in front of x²?

When you see $ x^2 $ with no visible coefficient, there's actually an invisible 1 in front of it. So $ x^2 = 1x^2 $, making a = 1.

Q: How do I remember which coefficient is which?

Use the pattern $ ax^2 + bx + c $: a goes with $ x^2 $, b goes with $ x $, and c is the number by itself (constant term).

Q: What if the equation is written in a different order?

Always rearrange the equation to match standard form first! Whether you see $ 4 + x^2 - 6x $ or $ -6x + x^2 + 4 $, rewrite it as $ x^2 - 6x + 4 $ before identifying coefficients.

Q: Can coefficients be negative?

Absolutely! Coefficients can be positive, negative, or even fractions. In our example, a = 1 (positive), b = -6 (negative), and c = 4 (positive).

Quadratic Coefficients with Standard Form

Identify the coefficients based on the following equation

$y=x^2-6x+4$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the function coefficients

00:04 We'll use the formula for representing a quadratic equation

00:10 We'll arrange the equation to match the formula

00:20 We'll separate the variable from the coefficient

00:29 We'll compare the formula to our equation and find the coefficients

00:39 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

Identify the coefficients based on the following equation

$y=x^2-6x+4$

Step-by-step solution

To solve this problem, we'll clearly delineate the given expression and compare it to the standard quadratic form:

Step 1: Recognize the standard form of a quadratic equation as $y = ax^2 + bx + c$ .
Step 2: Compare the given equation $y = x^2 - 6x + 4$ to the standard form.
Step 3: Identify coefficients:
- The coefficient of $x^2$ is $a = 1$ .
- The coefficient of $x$ is $b = -6$ .
- The constant term is $c = 4$ .

Therefore, the coefficients for the quadratic function $y = x^2 - 6x + 4$ are $a = 1$ , $b = -6$ , and $c = 4$ .

Among the provided choices, choice 3: $a=1,b=-6,c=4$ is the correct one.

Final Answer

$a=1,b=-6,c=4$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Always compare to $y = ax^2 + bx + c$
Technique: Identify coefficients by position: a=1, b=-6, c=4
Check: Rewrite equation maintaining signs: $x^2 + (-6)x + 4$ ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficient signs with operation signs
Don't mistake -6x as having coefficient b=6 because of the minus sign! This gives wrong identification of coefficients. Always remember that in $x^2 - 6x + 4$ , the coefficient of x is actually b=-6, not +6.

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 x equal to -6 and not +6?

In $y = x^2 - 6x + 4$ , we can rewrite this as $y = x^2 + (-6)x + 4$ . The coefficient is the number multiplying the variable, including its sign. So b = -6.

What if there's no number in front of x²?

When you see $x^2$ with no visible coefficient, there's actually an invisible 1 in front of it. So $x^2 = 1x^2$ , making a = 1.

How do I remember which coefficient is which?

Use the pattern $ax^2 + bx + c$ : a goes with $x^2$ , b goes with $x$ , and c is the number by itself (constant term).

What if the equation is written in a different order?

Always rearrange the equation to match standard form first! Whether you see $4 + x^2 - 6x$ or $-6x + x^2 + 4$ , rewrite it as $x^2 - 6x + 4$ before identifying coefficients.

Can coefficients be negative?

Absolutely! Coefficients can be positive, negative, or even fractions. In our example, a = 1 (positive), b = -6 (negative), and c = 4 (positive).

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Find Coefficients in the Quadratic Equation: y = x² - 6x + 4

Quadratic Coefficients with Standard Form

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is the coefficient of x equal to -6 and not +6?

What if there's no number in front of x²?

How do I remember which coefficient is which?

What if the equation is written in a different order?

Can coefficients be negative?

🌟 Unlock Your Math Potential

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