Identify Coefficients in y=-3x²-4: Quadratic Function Analysis

Q: Why is b = 0 when there's no x term in the equation?

In the standard form $ y = ax^2 + bx + c $, every coefficient must be identified. When there's no x term visible, it means the coefficient b equals zero, not that b doesn't exist!

Q: How do I remember which coefficient is which?

Use the pattern: a goes with $ x^2 $, b goes with $ x $, and c is the constant term (number by itself). Think: Always Before Constant!

Q: What if the equation is written differently, like y = -4 - 3x²?

First rearrange it to standard form: $ y = -3x^2 + 0x + (-4) $. The coefficients stay the same regardless of how the equation is initially written!

Q: Can coefficients be negative numbers?

Absolutely! Coefficients can be positive, negative, zero, or even fractions. In $ y = -3x^2 - 4 $, both a = -3 and c = -4 are negative.

Standard Form Identification with Missing Linear Term

Identify the coefficients based on the following equation

$y=-3x^2-4$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the function coefficients

00:03 Use the formula to represent a quadratic equation

00:13 Arrange the equation to match the formula

00:26 Separate the unknown from the coefficient

00:37 Compare the formula to our equation and find the coefficients

00:46 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

$y=-3x^2-4$

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Identify the form of a standard quadratic equation.
Step 2: Compare the given function with the quadratic standard form.
Step 3: Match the coefficients to the given answer choices.

Now, let's work through each step:
Step 1: The standard form of a quadratic function is $y = ax^2 + bx + c$ .
Step 2: Given the function $y = -3x^2 - 4$ , we compare this with the standard form:

Coefficient $a$ is associated with $x^2$ . Here, $a = -3$ .
Coefficient $b$ is associated with $x$ . Since there is no $x$ term, $b = 0$ .
The constant term $c$ is the standalone number, which is $c = -4$ .

Step 3: Given the coefficients

a = -3

b = 0

, and

c = -4

, match these with the choices provided. The correct choice is Choice 4:

a = -3, b = 0, c = -4

Therefore, the solution to the problem is $a = -3, b = 0, c = -4$ .

Final Answer

$a=-3,b=0,c=-4$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic equations follow $y = ax^2 + bx + c$ pattern
Coefficient Matching: Compare $y = -3x^2 - 4$ to find a = -3, b = 0, c = -4
Verification: Missing x term means b = 0, not that coefficient doesn't exist ✓

Common Mistakes

Avoid these frequent errors

Ignoring missing terms or forgetting zero coefficients
Don't skip the b coefficient just because there's no x term = incomplete answer! Students often think missing terms don't count as coefficients. Always identify all three coefficients a, b, and c, using b = 0 when the linear term is absent.

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 b = 0 when there's no x term in the equation?

In the standard form $y = ax^2 + bx + c$ , every coefficient must be identified. When there's no x term visible, it means the coefficient b equals zero, not that b doesn't exist!

How do I remember which coefficient is which?

Use the pattern: a goes with $x^2$ , b goes with $x$ , and c is the constant term (number by itself). Think: Always Before Constant!

What if the equation is written differently, like y = -4 - 3x²?

First rearrange it to standard form: $y = -3x^2 + 0x + (-4)$ . The coefficients stay the same regardless of how the equation is initially written!

Can coefficients be negative numbers?

Absolutely! Coefficients can be positive, negative, zero, or even fractions. In $y = -3x^2 - 4$ , both a = -3 and c = -4 are negative.

How can I check if my coefficients are correct?

Substitute your values back: if a = -3, b = 0, c = -4, then $ax^2 + bx + c = -3x^2 + 0x + (-4) = -3x^2 - 4$ ✓

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Identify Coefficients in y=-3x²-4: Quadratic Function Analysis

Standard Form Identification with Missing Linear Term

❤️ 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 b = 0 when there's no x term in the equation?

How do I remember which coefficient is which?

What if the equation is written differently, like y = -4 - 3x²?

Can coefficients be negative numbers?

How can I check if my coefficients are correct?

🌟 Unlock Your Math Potential

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