Analyze the Quadratic Function: y=-3x-4x²+3 in Standard Form

Q: Why do I need to rearrange the equation first?

The standard form $ ax^2 + bx + c $ has a specific order: highest power first, then middle power, then constant. Rearranging helps you match coefficients correctly to avoid confusion.

Q: What if there's no x² term visible?

Look carefully! In this problem, $ -4x^2 $ is there but comes after the x term. Always scan the entire equation for all powers of x.

Q: Can the coefficient 'a' be negative?

Absolutely! In this problem, a = -4 because the x² term is $ -4x^2 $. Negative coefficients are common and completely valid in quadratic functions.

Standard Form Coefficients with Rearranged Terms

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

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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

00:10 We'll arrange the equation to match the formula

00:38 We'll separate the unknown from the coefficient

00:52 We'll compare the formula to our equation and find the coefficients

00:58 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

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

Step-by-step solution

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

Step 1: Identify and write the standard form of a quadratic equation $y = ax^2 + bx + c$ .
Step 2: Compare the given function with the standard form to find the coefficients $a$ , $b$ , and $c$ .

Now, let's work through each step:

Step 1: The standard form of a quadratic equation is $y = ax^2 + bx + c$ .

Step 2: Comparing the given equation $y = -3x - 4x^2 + 3$ with the standard form:

The coefficient of $x^2$ is $-4$ , thus $a = -4$ .
The coefficient of $x$ is $-3$ , thus $b = -3$ .
The constant term is $3$ , thus $c = 3$ .

Therefore, the coefficients are $a = -4$ , $b = -3$ , $c = 3$ .

The correct option is: : $a=-4,b=-3,c=3$

Final Answer

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

Key Points to Remember

Essential concepts to master this topic

Standard Form: Always write as $ax^2 + bx + c$
Technique: Rearrange $-3x - 4x^2 + 3$ to $-4x^2 - 3x + 3$
Check: Coefficient of highest power term is a, then b, then c ✓

Common Mistakes

Avoid these frequent errors

Reading coefficients in the order they appear
Don't read coefficients as they appear in $-3x - 4x^2 + 3$ = wrong order! This gives wrong values like b = -4 instead of a = -4. Always rearrange to standard form $ax^2 + bx + c$ first, then identify 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 do I need to rearrange the equation first?

The standard form $ax^2 + bx + c$ has a specific order: highest power first, then middle power, then constant. Rearranging helps you match coefficients correctly to avoid confusion.

What if there's no x² term visible?

Look carefully! In this problem, $-4x^2$ is there but comes after the x term. Always scan the entire equation for all powers of x.

How do I remember which coefficient is which?

Use the pattern: a goes with x², b goes with x¹, c is the constant (no x). Think alphabetical order matches decreasing powers!

What if a term is missing?

If a term is missing, its coefficient is 0. For example, if there's no x term, then b = 0. Always account for missing terms when identifying coefficients.

Can the coefficient 'a' be negative?

Absolutely! In this problem, a = -4 because the x² term is $-4x^2$ . Negative coefficients are common and completely valid in quadratic functions.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 The Quadratic Function questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Analyze the Quadratic Function: y=-3x-4x²+3 in Standard Form

Standard Form Coefficients with Rearranged Terms

❤️ 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 do I need to rearrange the equation first?

What if there's no x² term visible?

How do I remember which coefficient is which?

What if a term is missing?

Can the coefficient 'a' be negative?

🌟 Unlock Your Math Potential

More Questions

Plotting Functions with Parameters

Find the Coefficients in y=5x-3x²: Polynomial Term Analysis

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

Coefficient Identification in y=-6+x²+6x: Breaking Down Terms

Find Coefficients in y=-x-3x²: Complete Polynomial Analysis

The function y=ax²+bx+c

Find Coefficients in the Equation y=3-x-x²: Step-by-Step Guide

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

Identify Coefficients in the Quadratic Function y=x²

Find Coefficients in the Equation y=-5x² + x: Step-by-Step Guide