Find the Constant Term c in y = -5x² + 4x - 3: Coefficient Analysis

Q: What does 'coefficient of the independent number' mean?

The independent number is the term that stands alone without any variable (like x). In $ y = -5x^2 + 4x - 3 $, the number -3 is independent because it has no x attached.

Q: Why isn't c equal to -5 since it's the first coefficient?

Position doesn't matter - only the variable power matters! The coefficient -5 belongs to $ x^2 $, so it's the 'a' value. The constant term c is always the number without any variable.

Q: What if the constant term is positive?

The sign is part of the coefficient! If you have $ y = -5x^2 + 4x + 3 $, then $ c = +3 $ or simply $ c = 3 $. Always include the sign.

Q: How do I remember which coefficient is which?

Think of alphabetical order by power: a goes with $ x^2 $ (highest power), b goes with $ x^1 $, and c goes with $ x^0 = 1 $ (the constant).

Q: What if a term is missing from the equation?

Missing terms have coefficient zero! For example, in $ y = x^2 - 7 $, there's no x term, so $ b = 0 $, but $ a = 1 $ and $ c = -7 $.

Quadratic Coefficients with Standard Form Identification

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

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

$y=-5x^2+4x-3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 First, let's find the coefficient C.

00:10 We'll use the quadratic equation formula. It's a powerful tool!

00:16 Now, compare this formula to our equation, and let's identify the coefficients.

00:26 We can see that coefficient C is the independent number.

00:31 And that's how we solve this problem!

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 $c$ in this quadratic equation:

$y=-5x^2+4x-3$

Step-by-step solution

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

Identify the given quadratic equation.
Compare the given equation with the standard quadratic form $ax^2 + bx + c$ .
Determine the value of $c$ by direct comparison.

Now, let's work through each step:
Step 1: The given quadratic equation is $y = -5x^2 + 4x - 3$ .
Step 2: The standard form of a quadratic equation is $ax^2 + bx + c$ . We need to match the coefficients accordingly.
Step 3: By comparing the terms from the equation with the standard form, $a$ is the coefficient of $x^2$ , $b$ is the coefficient of $x$ , and $c$ is the constant term or the independent number.

Therefore, from the equation $y = -5x^2 + 4x - 3$ :

$a = -5$
$b = 4$
$c = -3$

Thus, the value of $c$ in the quadratic equation is $c = -3$ .

Final Answer

$c=-3$

Key Points to Remember

Essential concepts to master this topic

Standard Form: $ax^2 + bx + c$ where c is the constant term
Technique: Match terms by degree: $-5x^2$ gives $a = -5$ , $4x$ gives $b = 4$
Check: Constant term has no variable, so $c = -3$ from the equation ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficient with constant term
Don't think c equals -5 or 4 just because they're larger numbers = wrong identification! The constant term is always the number without any variable attached. Always identify c as the independent number with no x.

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

What does 'coefficient of the independent number' mean?

The independent number is the term that stands alone without any variable (like x). In $y = -5x^2 + 4x - 3$ , the number -3 is independent because it has no x attached.

Why isn't c equal to -5 since it's the first coefficient?

Position doesn't matter - only the variable power matters! The coefficient -5 belongs to $x^2$ , so it's the 'a' value. The constant term c is always the number without any variable.

What if the constant term is positive?

The sign is part of the coefficient! If you have $y = -5x^2 + 4x + 3$ , then $c = +3$ or simply $c = 3$ . Always include the sign.

How do I remember which coefficient is which?

Think of alphabetical order by power: a goes with $x^2$ (highest power), b goes with $x^1$ , and c goes with $x^0 = 1$ (the constant).

What if a term is missing from the equation?

Missing terms have coefficient zero! For example, in $y = x^2 - 7$ , there's no x term, so $b = 0$ , but $a = 1$ and $c = -7$ .

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