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

Q: Why isn't a=5 since 5 comes first in the equation?

The order of terms doesn't matter for identifying coefficients! What matters is the degree of each term. Since $ 3x^2 $ is the highest degree term, its coefficient 3 becomes 'a'.

Q: What if there's no constant term like in this problem?

When there's no constant term, c = 0. This is common in quadratic functions that pass through the origin. The equation still follows standard form with c = 0.

Q: Do I need to rewrite the equation in order?

It's helpful but not required. You can identify coefficients from any order, but rewriting as $ y = 3x^2 + 5x + 0 $ makes it clearer to match with $ y = ax^2 + bx + c $.

Q: How do I remember which coefficient is which?

Use this memory trick: coefficients go in alphabetical order by degree! 'a' goes with x², 'b' goes with x¹, and 'c' goes with x⁰ (the constant).

Q: What if the x² term is negative?

The coefficient 'a' includes the sign! If you have $ y = -2x^2 + 3x + 1 $, then a = -2, not just 2. Always include positive or negative signs.

Quadratic Coefficients with Standard Form

Identify the coefficients based on the following equation

$y=5x+3x^2$

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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 We will use the formula to represent a quadratic equation

00:12 We will arrange the equation to match the formula

00:17 We will compare the formula to our equation and find the coefficients

00:44 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

$y=5x+3x^2$

Step-by-step solution

To solve this problem, we need to express the given function $y = 5x + 3x^2$ in the standard quadratic form $y = ax^2 + bx + c$ .

Let's match the components of $y = 5x + 3x^2$ with the standard form:

The term $3x^2$ corresponds to $ax^2$ , so $a = 3$ .
The term $5x$ corresponds to $bx$ , so $b = 5$ .
There is no constant term in the equation, which means $c = 0$ .

Therefore, the values of the coefficients are:

$a = 3$
$b = 5$
$c = 0$

From the answer choices given, the correct choice is:

Choice 3: $a = 3, b = 5, c = 0$

Therefore, the solution to the problem is $a = 3, b = 5, c = 0$ .

Final Answer

$a=3,b=5,c=0$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic equations follow $y = ax^2 + bx + c$ pattern
Identification: Match each term by degree: $3x^2$ gives a=3, $5x$ gives b=5
Verification: Expand $3x^2 + 5x + 0$ back to original form ✓

Common Mistakes

Avoid these frequent errors

Reading coefficients in order of appearance
Don't read y = 5x + 3x² as a=5, b=3, c=0! This ignores the degree of each term and gives wrong coefficients. Always match terms by their powers: x² term gives 'a', x term gives 'b', constant gives 'c'.

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 isn't a=5 since 5 comes first in the equation?

The order of terms doesn't matter for identifying coefficients! What matters is the degree of each term. Since $3x^2$ is the highest degree term, its coefficient 3 becomes 'a'.

What if there's no constant term like in this problem?

When there's no constant term, c = 0. This is common in quadratic functions that pass through the origin. The equation still follows standard form with c = 0.

Do I need to rewrite the equation in order?

It's helpful but not required. You can identify coefficients from any order, but rewriting as $y = 3x^2 + 5x + 0$ makes it clearer to match with $y = ax^2 + bx + c$ .

How do I remember which coefficient is which?

Use this memory trick: coefficients go in alphabetical order by degree! 'a' goes with x², 'b' goes with x¹, and 'c' goes with x⁰ (the constant).

What if the x² term is negative?

The coefficient 'a' includes the sign! If you have $y = -2x^2 + 3x + 1$ , then a = -2, not just 2. Always include positive or negative signs.

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

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 isn't a=5 since 5 comes first in the equation?

What if there's no constant term like in this problem?

Do I need to rewrite the equation in order?

How do I remember which coefficient is which?

What if the x² term is negative?

🌟 Unlock Your Math Potential

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