Constructing an Algebraic Expression: Using a = 4, b = 2, c = 1/2

Q: What does 'standard quadratic form' mean?

Standard quadratic form is $ ax^2 + bx + c $ where a is the coefficient of x², b is the coefficient of x, and c is the constant term.

Q: Why can't I use a different order for the terms?

The order matters for identification purposes! When we say a=4, b=2, c=1/2, these must go in their designated positions: $ 4x^2 + 2x + \frac{1}{2} $.

Q: How do I remember which coefficient goes where?

Think alphabetically: a comes first (with x²), b comes second (with x), c comes last (by itself). This matches the decreasing powers of x!

Q: Can I write the fraction differently?

Yes! $ \frac{1}{2} $ can also be written as 0.5, but keeping it as a fraction is usually clearer and more precise in algebraic expressions.

Standard Quadratic Form with Given Coefficients

Create an algebraic expression based on the following parameters:

$a=4,b=2,c=\frac{1}{2}$

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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 will use the formula to represent a quadratic equation

00:09 We will connect the parameter to the corresponding variable according to the formula

00:32 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:

$a=4,b=2,c=\frac{1}{2}$

Step-by-step solution

To solve this problem, we need to form a quadratic expression using given parameters in the standard form:

The standard quadratic function is represented as:

$y = ax^2 + bx + c$

Given parameters are:

$a = 4$
$b = 2$
$c = \frac{1}{2}$

We substitute these values into the standard quadratic expression:

$y = 4x^2 + 2x + \frac{1}{2}$

Thus, the algebraic expression we are looking for is $4x^2 + 2x + \frac{1}{2}$ .

Among the provided answer choices, the correct choice is:

Choice 3: $4x^2 + 2x + \frac{1}{2}$

The expression $4x^2 + 2x + \frac{1}{2}$ accurately represents the quadratic function with the given parameters.

Final Answer

$4x^2+2x+\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic expressions follow $ax^2 + bx + c$ pattern
Substitution: Replace a=4, b=2, c=1/2 to get $4x^2 + 2x + \frac{1}{2}$
Verification: Check coefficient order matches a, b, c values exactly ✓

Common Mistakes

Avoid these frequent errors

Mixing up coefficient positions or signs
Don't randomly place coefficients like $4x^2 - 2x + \frac{1}{2}$ = wrong expression! This changes the entire function's behavior. Always substitute coefficients in exact order: a goes with x², b goes with x, c stands alone.

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 does 'standard quadratic form' mean?

Standard quadratic form is $ax^2 + bx + c$ where a is the coefficient of x², b is the coefficient of x, and c is the constant term.

Why can't I use a different order for the terms?

The order matters for identification purposes! When we say a=4, b=2, c=1/2, these must go in their designated positions: $4x^2 + 2x + \frac{1}{2}$ .

What if one of the coefficients is negative?

Just substitute the negative value directly! For example, if b = -2, your expression becomes $4x^2 - 2x + \frac{1}{2}$ . The signs are part of the coefficients.

How do I remember which coefficient goes where?

Think alphabetically: a comes first (with x²), b comes second (with x), c comes last (by itself). This matches the decreasing powers of x!

Can I write the fraction differently?

Yes! $\frac{1}{2}$ can also be written as 0.5, but keeping it as a fraction is usually clearer and more precise in algebraic expressions.

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Constructing an Algebraic Expression: Using a = 4, b = 2, c = 1/2

Standard Quadratic Form with Given 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 does 'standard quadratic form' mean?

Why can't I use a different order for the terms?

What if one of the coefficients is negative?

How do I remember which coefficient goes where?

Can I write the fraction differently?

🌟 Unlock Your Math Potential

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