Identify Coefficients in y=3x²+4x+5: Quadratic Equation Analysis

Q: What if there's no x² term in the equation?

If there's no $ x^2 $ term visible, then a = 0 and it's actually a linear equation, not quadratic! A true quadratic must have $ a \neq 0 $.

Q: What if a term is missing, like no x term?

Missing terms have a coefficient of 0. For example, $ y = 2x^2 + 7 $ means a = 2, b = 0, c = 7 since there's no x term.

Q: Do I include the plus and minus signs?

Yes! Signs are part of the coefficient. In $ y = -3x^2 + 4x - 5 $, we have a = -3, b = 4, c = -5. Pay close attention to negative signs!

Q: How do I remember which coefficient is which?

Remember alphabetical order: 'a' goes with the highest power (x²), 'b' goes with the middle power (x¹), and 'c' goes with the lowest power (x⁰ = constant).

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

First rearrange the terms! Put the $ x^2 $ term first, then the $ x $ term, then the constant. For example, $ y = 5 + 2x - x^2 $ becomes $ y = -x^2 + 2x + 5 $.

Quadratic Coefficients with Standard Form

Identify the coefficients based on the following equation

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

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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'll use the formula to represent a quadratic equation

00:15 We'll separate the variable from the coefficient

00:32 We'll compare the formula to our equation and find the coefficients

00:38 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

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

Step-by-step solution

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

Step 1: Identify the given quadratic function.
Step 2: Compare it to the standard form $y = ax^2 + bx + c$ .
Step 3: Determine the values of $a$ , $b$ , and $c$ .

Now, let's work through each step:

Step 1: The problem gives us the quadratic function $y = 3x^2 + 4x + 5$ .

Step 2: The standard form of a quadratic function is $y = ax^2 + bx + c$ .

Step 3: By comparing $y = 3x^2 + 4x + 5$ with $y = ax^2 + bx + c$ , we find:
- The coefficient of $x^2$ is $a = 3$ .
- The coefficient of $x$ is $b = 4$ .
- The constant term is $c = 5$ .

Therefore, the solution to the problem is $a = 3, b = 4, c = 5$ .

This matches choice 2, which states: $a = 3, b = 4, c = 5$ .

Final Answer

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

Key Points to Remember

Essential concepts to master this topic

Standard Form: Every quadratic follows the pattern $y = ax^2 + bx + c$
Pattern Matching: Compare term by term: $3x^2$ means $a = 3$
Verification: Substitute back: $3x^2 + 4x + 5 = ax^2 + bx + c$ confirms coefficients ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficient order or signs
Don't mix up the order like writing a = 5, b = 4, c = 3 or changing signs like a = -3! This happens when you don't carefully match each term's position. Always identify coefficients by matching the exact position: 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

What if there's no x² term in the equation?

If there's no $x^2$ term visible, then a = 0 and it's actually a linear equation, not quadratic! A true quadratic must have $a \neq 0$ .

What if a term is missing, like no x term?

Missing terms have a coefficient of 0. For example, $y = 2x^2 + 7$ means a = 2, b = 0, c = 7 since there's no x term.

Do I include the plus and minus signs?

Yes! Signs are part of the coefficient. In $y = -3x^2 + 4x - 5$ , we have a = -3, b = 4, c = -5. Pay close attention to negative signs!

How do I remember which coefficient is which?

Remember alphabetical order: 'a' goes with the highest power (x²), 'b' goes with the middle power (x¹), and 'c' goes with the lowest power (x⁰ = constant).

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

First rearrange the terms! Put the $x^2$ term first, then the $x$ term, then the constant. For example, $y = 5 + 2x - x^2$ becomes $y = -x^2 + 2x + 5$ .

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Identify Coefficients in y=3x²+4x+5: Quadratic Equation 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

What if there's no x² term in the equation?

What if a term is missing, like no x term?

Do I include the plus and minus signs?

How do I remember which coefficient is which?

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

🌟 Unlock Your Math Potential

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