Find the x² Coefficient in y=3x+30: Linear vs Quadratic Analysis

Q: Why isn't this equation quadratic if it asks for coefficient a?

The question is actually testing your understanding of equation types! Just because it asks for the coefficient of $ x^2 $ doesn't mean the equation contains that term.

Q: What makes an equation quadratic vs linear?

A quadratic equation must have an $ x^2 $ term (highest power is 2). A linear equation has $ x $ as the highest power (power is 1). $ y = 3x + 30 $ is linear because the highest power is 1.

Q: Could the coefficient a be zero in this case?

Technically, you could say $ a = 0 $ since $ 0x^2 = 0 $, but that's not really a quadratic equation anymore. When $ a = 0 $ in $ ax^2 + bx + c $, it becomes linear!

Q: How can I quickly identify equation types?

Look for the highest power of the variable:Power 1 (like $ 3x $): LinearPower 2 (like $ 2x^2 $): QuadraticPower 3 (like $ x^3 $): Cubic

Q: What if I see y = instead of = 0?

The form doesn't matter! Whether it's $ y = 3x + 30 $ or $ 3x + 30 = 0 $, both are linear because the highest power of x is 1.

Linear Equations with Quadratic Misidentification

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $a$ in this quadratic equation:

$y=3x+30$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find coefficient A

00:03 We'll use the quadratic equation formula

00:11 We can see that coefficient A is for the X squared term

00:14 In this equation we don't have X squared, meaning it has a coefficient of 0

00:21 Let's compare the formula to our equation and find the coefficients

00:34 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

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $a$ in this quadratic equation:

$y=3x+30$

Step-by-step solution

The given equation is $y = 3x + 30$ . This equation does not include a term involving $x^2$ , meaning it is not a quadratic equation. A quadratic equation is typically of the form $ax^2 + bx + c = 0$ and includes an $x^2$ term.

Let's compare:

The general form of a quadratic equation: $ax^2 + bx + c$
Our equation: $y = 3x + 30$

By observation, the given equation does not have an $x^2$ term. Therefore, there can be no coefficient $a$ because it would need to be a coefficient of an $x^2$ component that does not exist in this equation.

Therefore, this is not a quadratic equation.

The correct choice is: "That's not a quadratic equation."

Final Answer

That's not a quadratic equation

Key Points to Remember

Essential concepts to master this topic

Definition: Quadratic equations must contain an $x^2$ term
Identification: $y = 3x + 30$ has no $x^2$ term, making it linear
Check: Count the highest power of x: power 1 = linear, power 2 = quadratic ✓

Common Mistakes

Avoid these frequent errors

Assuming all equations with coefficients a, b, c are quadratic
Don't assign coefficient values when the corresponding term doesn't exist = wrong equation type! Just because we define a as the coefficient of $x^2$ doesn't mean every equation has an $x^2$ term. Always check if the $x^2$ term actually exists before calling it quadratic.

Practice Quiz

Test your knowledge with interactive questions

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $$ a $$ in the equation

$$ y=3x-10+5x^2 $$

FAQ

Everything you need to know about this question

Why isn't this equation quadratic if it asks for coefficient a?

The question is actually testing your understanding of equation types! Just because it asks for the coefficient of $x^2$ doesn't mean the equation contains that term.

What makes an equation quadratic vs linear?

A quadratic equation must have an $x^2$ term (highest power is 2). A linear equation has $x$ as the highest power (power is 1). $y = 3x + 30$ is linear because the highest power is 1.

Could the coefficient a be zero in this case?

Technically, you could say $a = 0$ since $0x^2 = 0$ , but that's not really a quadratic equation anymore. When $a = 0$ in $ax^2 + bx + c$ , it becomes linear!

How can I quickly identify equation types?

Look for the highest power of the variable:

Power 1 (like $3x$ ): Linear
Power 2 (like $2x^2$ ): Quadratic
Power 3 (like $x^3$ ): Cubic

What if I see y = instead of = 0?

The form doesn't matter! Whether it's $y = 3x + 30$ or $3x + 30 = 0$ , both are linear because the highest power of x is 1.

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