Find Coefficients in y = 3x² + 4 - 5x: Term-by-Term Analysis

Q: Why can't I just read the coefficients in the order given?

The standard form has a specific order: $ ax^2 + bx + c $. If terms are mixed up like $ 3x^2 + 4 - 5x $, you need to rearrange them first to match this pattern.

Q: How do I know which term goes where?

Look at the degree of each term: $ x^2 $ terms go first, $ x $ terms go second, and constant terms (no variables) go last.

Q: What if there's no x term in the equation?

That's fine! If there's no $ x $ term, then b = 0. For example, $ y = 2x^2 + 7 $ has a=2, b=0, c=7.

Q: Why is the coefficient of x negative in this problem?

Because the original equation has -5x (negative 5x). When we rearrange to standard form, this becomes the b coefficient, so b = -5.

Q: Can I check my answer somehow?

Yes! Substitute your coefficients back: $ 3x^2 + (-5)x + 4 = 3x^2 - 5x + 4 $. This should match your rearranged equation exactly.

Standard Form Coefficients with Rearrangement

Identify the coefficients based on the following equation

$y=3x^2+4-5x$

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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 Use the formula to represent a quadratic equation

00:11 Arrange the equation to match the formula

00:34 Separate the unknown from the coefficient

00:46 Compare the formula to our equation and find the coefficients

00:56 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

$y=3x^2+4-5x$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Rearrange the given quadratic function into the standard form.
Step 2: Identify the coefficients by comparing them with the standard quadratic function.

Now let's work through each step:

Step 1: The given quadratic is $y = 3x^2 + 4 - 5x$ . Rearrange this function to align terms with their degrees:
$y = 3x^2 - 5x + 4$ .

Step 2: Compare this with the standard quadratic form $y = ax^2 + bx + c$ , where:
$a = 3$ (the coefficient of $x^2$ ),
$b = -5$ (the coefficient of $x$ ),
$c = 4$ (the constant term).

Therefore, the correct choice is $a = 3, b = -5, c = 4$ .

Final Answer

$a=3,b=-5,c=4$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Rearrange as $ax^2 + bx + c$ to identify coefficients
Technique: Rewrite $3x^2 + 4 - 5x$ as $3x^2 - 5x + 4$
Check: Verify a=3, b=-5, c=4 matches rearranged form exactly ✓

Common Mistakes

Avoid these frequent errors

Reading coefficients from the original unsorted equation
Don't identify coefficients from $3x^2 + 4 - 5x$ directly = wrong b and c values! The terms must be in degree order first. Always rearrange to standard form $ax^2 + bx + c$ before identifying coefficients.

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 can't I just read the coefficients in the order given?

The standard form has a specific order: $ax^2 + bx + c$ . If terms are mixed up like $3x^2 + 4 - 5x$ , you need to rearrange them first to match this pattern.

How do I know which term goes where?

Look at the degree of each term: $x^2$ terms go first, $x$ terms go second, and constant terms (no variables) go last.

What if there's no x term in the equation?

That's fine! If there's no $x$ term, then b = 0. For example, $y = 2x^2 + 7$ has a=2, b=0, c=7.

Why is the coefficient of x negative in this problem?

Because the original equation has -5x (negative 5x). When we rearrange to standard form, this becomes the b coefficient, so b = -5.

Can I check my answer somehow?

Yes! Substitute your coefficients back: $3x^2 + (-5)x + 4 = 3x^2 - 5x + 4$ . This should match your rearranged equation exactly.

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Find Coefficients in y = 3x² + 4 - 5x: Term-by-Term Analysis

Standard Form Coefficients with Rearrangement

❤️ 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 can't I just read the coefficients in the order given?

How do I know which term goes where?

What if there's no x term in the equation?

Why is the coefficient of x negative in this problem?

Can I check my answer somehow?

🌟 Unlock Your Math Potential

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