Find the Coefficients in y=5x²-4x-30: Quadratic Equation Analysis

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

Always rearrange first! Move all terms to one side so you have $ y = ax^2 + bx + c $. Then identify coefficients by matching each term.

Q: What if there's no x term or constant term?

Missing terms have a coefficient of 0. For example, in $ y = 3x^2 - 7 $, there's no x term, so b = 0.

Q: Do I include the negative sign as part of the coefficient?

Yes, absolutely! The sign is part of the coefficient. In $ -4x $, the coefficient is -4, not just 4.

Q: How can I remember which coefficient is which?

Remember alphabetical order: 'a' goes with x², 'b' goes with x¹, and 'c' is the constant (x⁰). The powers decrease as you go through the alphabet!

Q: What if the x² term comes last in the equation?

The position doesn't matter - only the variable part matters! Whether it's $ 5x^2 - 4x - 30 $ or $ -30 - 4x + 5x^2 $, the coefficient of x² is still 5.

Quadratic Coefficients with Standard Form

Identify the coefficients based on the following equation

$y=5x^2-4x-30$

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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

00:19 We'll separate the variable from the coefficient

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

00:40 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

$y=5x^2-4x-30$

Step-by-step solution

The given quadratic function is $y = 5x^2 - 4x - 30$ .
To identify the coefficients, let's compare this with the standard form of a quadratic equation, $y = ax^2 + bx + c$ .

Step 1: Compare the terms of the given equation to the standard form.
Step 2: Identify each coefficient:
For $ax^2$ , $a = 5$ in the term $5x^2$ .
For $bx$ , $b = -4$ in the term $-4x$ .
For the constant term $c$ , $c = -30$ .

Thus, we have identified the coefficients as $a = 5$ , $b = -4$ , and $c = -30$ .

Therefore, the correct answer is $a = 5, b = -4, c = -30$ .

The correct choice is .

Final Answer

$a=5,b=-4,c=-30$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Compare $y = ax^2 + bx + c$ to identify coefficients
Technique: Match terms directly: $5x^2$ gives a = 5, $-4x$ gives b = -4
Check: Substitute back: $y = 5x^2 + (-4)x + (-30)$ matches original ✓

Common Mistakes

Avoid these frequent errors

Confusing the order or signs of coefficients
Don't mix up which coefficient goes with which term or ignore negative signs = wrong identification like a = -4! The coefficient of x² is always 'a', the coefficient of x is always 'b', and the constant is always 'c'. Always match each term carefully to the standard form $ax^2 + bx + c$ .

Practice Quiz

Test your knowledge with interactive questions

What is the value of the coefficient $$ b $$ in the equation below?

$$ 3x^2+8x-5 $$

FAQ

Everything you need to know about this question

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

Always rearrange first! Move all terms to one side so you have $y = ax^2 + bx + c$ . Then identify coefficients by matching each term.

What if there's no x term or constant term?

Missing terms have a coefficient of 0. For example, in $y = 3x^2 - 7$ , there's no x term, so b = 0.

Do I include the negative sign as part of the coefficient?

Yes, absolutely! The sign is part of the coefficient. In $-4x$ , the coefficient is -4, not just 4.

How can I remember which coefficient is which?

Remember alphabetical order: 'a' goes with x², 'b' goes with x¹, and 'c' is the constant (x⁰). The powers decrease as you go through the alphabet!

What if the x² term comes last in the equation?

The position doesn't matter - only the variable part matters! Whether it's $5x^2 - 4x - 30$ or $-30 - 4x + 5x^2$ , the coefficient of x² is still 5.

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Find the Coefficients in y=5x²-4x-30: 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 the equation isn't written in standard form?

What if there's no x term or constant term?

Do I include the negative sign as part of the coefficient?

How can I remember which coefficient is which?

What if the x² term comes last in the equation?

🌟 Unlock Your Math Potential

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