Formulate an Algebraic Expression with Parameters: a=0, b=2, c=4

Q: What happens when a coefficient equals zero?

When any coefficient equals zero, that entire term disappears from the expression! Zero times any variable equals zero, so $ 0 \cdot x^2 = 0 $ and gets eliminated.

Q: Is this still a quadratic function if a = 0?

No! When a = 0, you get a linear function instead. Quadratic functions must have an $ x^2 $ term, so this becomes $ y = 2x + 4 $.

Q: Should I write 0x² in my final answer?

Never! Always simplify by removing zero terms completely. Writing $ 0x^2 + 2x + 4 $ is mathematically correct but not simplified. The clean answer is just $ 2x + 4 $.

Q: How do I substitute the values correctly?

Replace each letter with its given value: $ a = 0 $, $ b = 2 $, $ c = 4 $. So $ ax^2 + bx + c $ becomes $ 0 \cdot x^2 + 2x + 4 $.

Q: What if multiple coefficients were zero?

Apply the same rule to all zero coefficients! If both a and b were zero, you'd have just $ y = c $, which is a constant function.

Quadratic Functions with Zero Coefficients

Create an algebraic expression based on the following parameters:

$a=0,b=2,c=4$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert the parameters to a quadratic function

00:03 We'll use the formula to represent a quadratic equation

00:15 Connect the parameter to its corresponding variable according to the formula

00:35 Write the function in its simplified form

00:50 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

Create an algebraic expression based on the following parameters:

$a=0,b=2,c=4$

Step-by-step solution

To solve this problem, we must recognize that we are given parameters for a quadratic function defined by the expression $y = ax^2 + bx + c$ .

Given:

$a = 0$
$b = 2$
$c = 4$

Step 1: Start with the general form of a quadratic function: $y = ax^2 + bx + c$ .

Step 2: Substitute the given values of $a$ , $b$ , and $c$ into the expression.

So, we have:

$y = 0 \cdot x^2 + 2x + 4$

Step 3: Simplify the expression.

The term $0 \cdot x^2$ equals 0, and therefore, it drops out of the expression. This results in:

$y = 2x + 4$

This is the algebraic expression based on the parameters provided. Thus, the correct choice from the options given is:

$2x + 4$ , which corresponds to choice $2$ .

Final Answer

$2x+4$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic functions follow $ax^2 + bx + c$ format
Zero Coefficient: When a = 0, the $x^2$ term disappears completely
Verification: Substitute back: 0(x²) + 2x + 4 = 2x + 4 ✓

Common Mistakes

Avoid these frequent errors

Including the x² term when a = 0
Don't write $0x^2 + 2x + 4$ as your final answer! Zero times anything equals zero, so the entire $x^2$ term vanishes. Always simplify by removing terms that equal zero completely.

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 a coefficient equals zero?

When any coefficient equals zero, that entire term disappears from the expression! Zero times any variable equals zero, so $0 \cdot x^2 = 0$ and gets eliminated.

Is this still a quadratic function if a = 0?

No! When a = 0, you get a linear function instead. Quadratic functions must have an $x^2$ term, so this becomes $y = 2x + 4$ .

Should I write 0x² in my final answer?

Never! Always simplify by removing zero terms completely. Writing $0x^2 + 2x + 4$ is mathematically correct but not simplified. The clean answer is just $2x + 4$ .

How do I substitute the values correctly?

Replace each letter with its given value: $a = 0$ , $b = 2$ , $c = 4$ . So $ax^2 + bx + c$ becomes $0 \cdot x^2 + 2x + 4$ .

What if multiple coefficients were zero?

Apply the same rule to all zero coefficients! If both a and b were zero, you'd have just $y = c$ , which is a constant function.

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Formulate an Algebraic Expression with Parameters: a=0, b=2, c=4

Quadratic Functions with Zero Coefficients

❤️ 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 a coefficient equals zero?

Is this still a quadratic function if a = 0?

Should I write 0x² in my final answer?

How do I substitute the values correctly?

What if multiple coefficients were zero?

🌟 Unlock Your Math Potential

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