Create Algebraic Expressions: Using a=4, b=-16, c=0

Q: What happens when c = 0 in a quadratic expression?

When c = 0, the constant term disappears! Your expression becomes $ ax^2 + bx $ instead of having three terms. This is still a valid quadratic expression.

Q: Why does b = -16 become -16x instead of +16x?

The coefficient includes the sign! When b = -16, you substitute the entire value including the negative sign. So $ bx $ becomes $ (-16)x = -16x $.

Q: Can I factor this expression further?

Yes! You can factor out the common term: $ 4x^2 - 16x = 4x(x - 4) $. Both forms are correct, but the question asks for the standard expanded form.

Q: What if I mixed up the order of terms?

The standard order is highest degree first: $ x^2 $ term, then $ x $ term, then constant. So $ 4x^2 - 16x $ is correct, not $ -16x + 4x^2 $.

Quadratic Expressions with Zero Constant Term

Create an algebraic expression based on the following parameters:

$a=4,b=-16,c=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's convert the parameters into a quadratic function.

00:12 We start by associating each parameter with the right variable using the formula.

00:25 Now, let's write our function in its simplest form.

00:45 And that's how we find the solution to this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Create an algebraic expression based on the following parameters:

$a=4,b=-16,c=0$

Step-by-step solution

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

Step 1: Formulate using the standard quadratic expression template.
Step 2: Substitute the given parameters.
Step 3: Simplify the resultant expression.

Now, let's work through each step:

Step 1: We use the standard form of a quadratic expression, which is $ax^2 + bx + c$ .

Step 2: Substitute the values $a = 4$ , $b = -16$ , and $c = 0$ into this template:

$ax^2 + bx + c \rightarrow 4x^2 - 16x + 0$

Step 3: Simplify the expression:

The expression simplifies to $4x^2 - 16x$ .

Thus, the algebraic expression based on the given parameters is $4x^2 - 16x$ .

Checking against the answer choices, the correct choice is: $4x^2 - 16x$ .

Final Answer

$4x^2-16x$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Use the template $ax^2 + bx + c$ with given coefficients
Substitution: Replace a=4, b=-16, c=0 to get $4x^2 - 16x + 0$
Simplification: Remove zero terms to get final form $4x^2 - 16x$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to include the sign when substituting negative coefficients
Don't write $4x^2 + 16x$ when b = -16! This creates a completely different expression with positive 16x instead of negative. Always pay careful attention to the signs when b = -16 becomes -16x in the expression.

Practice Quiz

Test your knowledge with interactive questions

What is the value of the coefficient $$ b $$ in the equation below?

$$ 3x^2+8x-5 $$

FAQ

Everything you need to know about this question

What happens when c = 0 in a quadratic expression?

When c = 0, the constant term disappears! Your expression becomes $ax^2 + bx$ instead of having three terms. This is still a valid quadratic expression.

Why does b = -16 become -16x instead of +16x?

The coefficient includes the sign! When b = -16, you substitute the entire value including the negative sign. So $bx$ becomes $(-16)x = -16x$ .

How do I know which answer choice is correct?

Compare your simplified expression with each option. Look for exact matches in coefficients and signs. In this case, $4x^2 - 16x$ matches choice 3 perfectly.

Can I factor this expression further?

Yes! You can factor out the common term: $4x^2 - 16x = 4x(x - 4)$ . Both forms are correct, but the question asks for the standard expanded form.

What if I mixed up the order of terms?

The standard order is highest degree first: $x^2$ term, then $x$ term, then constant. So $4x^2 - 16x$ is correct, not $-16x + 4x^2$ .

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Create Algebraic Expressions: Using a=4, b=-16, c=0

Quadratic Expressions with Zero Constant Term

❤️ 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

What happens when c = 0 in a quadratic expression?

Why does b = -16 become -16x instead of +16x?

How do I know which answer choice is correct?

Can I factor this expression further?

What if I mixed up the order of terms?

🌟 Unlock Your Math Potential

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