Find Coefficients in y=-40x+40: Linear Equation Analysis

Q: Why is 'a' equal to 0 if there's no x² term?

In the standard form $ ax^2 + bx + c $, the coefficient 'a' belongs to the $ x^2 $ term. When there's no $ x^2 $ term, it's like having $ 0 \cdot x^2 $, so a = 0.

Q: How do I remember which coefficient is which?

Think alphabetically: 'a' goes with the highest power ($ x^2 $), 'b' with the middle power ($ x^1 $), and 'c' with the lowest power (constant). It's like counting down!

Q: What if the equation is written differently like 40 - 40x?

Always rearrange to standard form first! $ y = 40 - 40x $ becomes $ y = -40x + 40 $. Then identify: a = 0, b = -40, c = 40.

Q: Can a linear equation really fit the quadratic form?

Absolutely! A linear equation is just a special case of a quadratic where the $ x^2 $ coefficient is zero. Every linear function can be written in quadratic form.

Q: Why is the constant term called 'c'?

The constant term 'c' is the y-intercept - where the line crosses the y-axis. In $ y = -40x + 40 $, when x = 0, y = 40, so c = 40.

Quadratic Form Coefficients with Linear Functions

Identify the coefficients based on the following equation

$y=-40x+40$

❤️ 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

00:13 Let's arrange the equation to match the formula

00:39 Let's separate the variable from the coefficient

00:55 We'll compare the formula to our equation and find the coefficients

01:07 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

$y=-40x+40$

Step-by-step solution

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

Identify the equation as a linear function represented in the form of $y = ax^2 + bx + c$ , where $a$ , $b$ , and $c$ are coefficients we need to find.
Recognize that since the function is linear and lacks an $x^2$ term, $a$ must be $0$ .
Match the coefficient of $x$ with $b$ .
Match the constant term with $c$ .

Now, let's work through each step:
Step 1: Our equation is $y = -40x + 40$ . It doesn't have an $x^2$ term, so $a = 0$ .
Step 2: The coefficient of $x$ is $-40$ , which corresponds to $b$ . Thus, $b = -40$ .
Step 3: The constant term is $40$ , which corresponds to $c$ . Thus, $c = 40$ .

Therefore, the solution to the problem is $a = 0, b = -40, c = 40$ .

The correct choice from the provided options is :

$a=0,b=-40,c=40$

Final Answer

$a=0,b=-40,c=40$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Express as $ax^2 + bx + c$ to identify coefficients clearly
Technique: Missing $x^2$ term means $a = 0$ in $y = -40x + 40$
Check: Rewrite as $y = 0x^2 + (-40)x + 40$ confirms $a=0, b=-40, c=40$ ✓

Common Mistakes

Avoid these frequent errors

Confusing linear and quadratic coefficient positions
Don't assign the x-coefficient (-40) to position 'a' just because it's the first term = wrong identification! The 'a' coefficient is always for the x² term. Always remember that a linear function like y = -40x + 40 has no x² term, so a = 0.

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 'a' equal to 0 if there's no x² term?

In the standard form $ax^2 + bx + c$ , the coefficient 'a' belongs to the $x^2$ term. When there's no $x^2$ term, it's like having $0 \cdot x^2$ , so a = 0.

How do I remember which coefficient is which?

Think alphabetically: 'a' goes with the highest power ( $x^2$ ), 'b' with the middle power ( $x^1$ ), and 'c' with the lowest power (constant). It's like counting down!

What if the equation is written differently like 40 - 40x?

Always rearrange to standard form first! $y = 40 - 40x$ becomes $y = -40x + 40$ . Then identify: a = 0, b = -40, c = 40.

Can a linear equation really fit the quadratic form?

Absolutely! A linear equation is just a special case of a quadratic where the $x^2$ coefficient is zero. Every linear function can be written in quadratic form.

Why is the constant term called 'c'?

The constant term 'c' is the y-intercept - where the line crosses the y-axis. In $y = -40x + 40$ , when x = 0, y = 40, so c = 40.

🌟 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

Find Coefficients in y=-40x+40: Linear Equation Analysis

Quadratic Form Coefficients with Linear Functions

❤️ 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 'a' equal to 0 if there's no x² term?

How do I remember which coefficient is which?

What if the equation is written differently like 40 - 40x?

Can a linear equation really fit the quadratic form?

Why is the constant term called 'c'?

🌟 Unlock Your Math Potential

More Questions

The function y=ax²+bx+c

Find Coefficients in y=-x² + 3x + 40: Quadratic Equation Analysis

Find Coefficients in y = 3x² - 81: Quadratic Equation Analysis

Find Coefficients in the Linear Equation y=6-3x: Step-by-Step

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

Plotting Functions with Parameters

Identify Coefficients in y=6x+3x²-4: Polynomial Term Analysis

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

Find Coefficients in y=-4x²-3x: Quadratic Expression Analysis

Find Coefficients in y=44-11x: Linear Equation Analysis