Find the Missing Coefficient b in the Quadratic Equation y = 4x² - 16

Q: What if there's no x term written in the equation?

When there's no x term visible, it means the coefficient of x is zero! Think of it as $ 4x^2 + 0x - 16 $ - the 0x term is just not written because 0 times anything equals 0.

Q: How do I remember which coefficient is which?

Use the standard form $ ax^2 + bx + c $ as your guide:a = coefficient of $ x^2 $b = coefficient of $ x $c = constant (no variable)

Q: Can b ever be negative?

Absolutely! The coefficient b can be positive, negative, or zero. For example, in $ x^2 - 3x + 2 $, we have b = -3. In our problem, b happens to be 0.

Q: What's the difference between incomplete and complete quadratics?

A complete quadratic has all three terms: $ ax^2 + bx + c $. An incomplete quadratic is missing one or more terms. Our equation $ y = 4x^2 - 16 $ is incomplete because it's missing the x term (b = 0).

Quadratic Coefficients with Missing Linear Terms

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

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

$y=4x^2-16$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find coefficient B

00:03 We'll use the quadratic equation formula

00:07 We can see that coefficient B is for the X term

00:15 In this equation we don't have an X term, meaning it's multiplied by 0

00:19 Let's compare the formula to our equation and find the coefficients:

00:31 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 $b$ in this quadratic equation:

$y=4x^2-16$

Step-by-step solution

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

Identify the given information and the standard quadratic form
Compare the given equation to this standard form
Extract the coefficients $a$ , $b$ , and $c$ and find $b$

Now, let's work through each step:
Step 1: The problem provides us with the equation $y = 4x^2 - 16$ . It's already in a form where we can identify the coefficients.
Step 2: Recall the standard form of a quadratic equation is $ax^2 + bx + c$ . Compare this form to the equation $y = 4x^2 - 16$ .
Step 3: By comparison, the coefficient of $x^2$ (which is $a$ ) is 4. There is no $x$ term explicitly present, implying that $b = 0$ . The constant $c$ is -16.
Therefore, after comparison and identification, it becomes clear that the value of $b$ in the equation is $b = 0$ .

Final Answer

$b=0$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic equations follow $ax^2 + bx + c$ pattern
Missing Terms: When $y = 4x^2 - 16$ , the x term coefficient is 0
Verification: Rewrite as $4x^2 + 0x - 16$ to confirm b = 0 ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficients with constant terms
Don't think b = -16 because -16 appears in the equation! The coefficient b only applies to the x term, not the constant. Always identify which variable each number multiplies - here -16 is the constant c, not coefficient b.

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 b equal to -16 if -16 is in the equation?

The coefficient b is specifically the number that multiplies the $x$ term. Since $y = 4x^2 - 16$ has no x term, b = 0. The -16 is the constant term c, not b!

What if there's no x term written in the equation?

When there's no x term visible, it means the coefficient of x is zero! Think of it as $4x^2 + 0x - 16$ - the 0x term is just not written because 0 times anything equals 0.

How do I remember which coefficient is which?

Use the standard form $ax^2 + bx + c$ as your guide:

a = coefficient of $x^2$
b = coefficient of $x$
c = constant (no variable)

Can b ever be negative?

Absolutely! The coefficient b can be positive, negative, or zero. For example, in $x^2 - 3x + 2$ , we have b = -3. In our problem, b happens to be 0.

What's the difference between incomplete and complete quadratics?

A complete quadratic has all three terms: $ax^2 + bx + c$ . An incomplete quadratic is missing one or more terms. Our equation $y = 4x^2 - 16$ is incomplete because it's missing the x term (b = 0).

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