Formulate an Algebraic Expression with Constants: a=2, b=1/2, c=4

Q: What does each letter represent in the quadratic form?

In $ ax^2 + bx + c $, a is the coefficient of x², b is the coefficient of x, and c is the constant term with no variable.

Q: Why is the fraction 1/2 kept as a fraction instead of converted to decimal?

Keeping $ \frac{1}{2} $ as a fraction is more precise than 0.5 and shows the exact value. Fractions are preferred in algebraic expressions unless specifically asked for decimals.

Q: Can I rearrange the terms in a different order?

Yes! $ 2x^2 + \frac{1}{2}x + 4 $ equals $ \frac{1}{2}x + 2x^2 + 4 $, but standard form puts the highest degree term first (x²), then x, then the constant.

Q: What if one of the coefficients was zero?

If a coefficient is zero, that term disappears from the expression. For example, if b=0, you'd get $ 2x^2 + 4 $ (no x term).

Q: How do I check if my expression is correct?

Compare each part: the coefficient of x² should be a=2, the coefficient of x should be b=1/2, and the constant should be c=4.

Quadratic Expressions with Given Coefficients

Create an algebraic expression based on the following parameters:

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

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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

00:13 Connect the parameter to its corresponding unknown according to the formula

00:37 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:

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

Step-by-step solution

To solve this problem, we'll follow the steps outlined:

Step 1: Identify the given values for the quadratic function's parameters: $a = 2$ , $b = \frac{1}{2}$ , and $c = 4$ .
Step 2: Apply these values to the standard quadratic form $y = ax^2 + bx + c$ .
Step 3: Substitute the values to construct the algebraic expression.

Now, let's proceed with these steps:

Given the standard form of a quadratic expression $y = ax^2 + bx + c$ :

Substituting the values, we obtain:

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

Therefore, the correct algebraic expression for the quadratic function is $2x^2 + \frac{1}{2}x + 4$ .

Final Answer

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

Key Points to Remember

Essential concepts to master this topic

Standard Form: Use $ax^2 + bx + c$ with given values
Substitution: Replace a=2, b=1/2, c=4 to get $2x^2 + \frac{1}{2}x + 4$
Verification: Check each coefficient matches: a=2 in $2x^2$ , b=1/2 in $\frac{1}{2}x$ , c=4 constant ✓

Common Mistakes

Avoid these frequent errors

Mixing up the order of coefficients
Don't place coefficients in wrong positions like putting b=1/2 as the coefficient of x² = $\frac{1}{2}x^2 + 2x + 4$ ! This changes the entire quadratic function. Always match coefficients to their correct terms: a goes with x², b with x, and c stands alone.

Practice Quiz

Test your knowledge with interactive questions

Identify the coefficients based on the following equation

$$ y=x^2 $$

FAQ

Everything you need to know about this question

What does each letter represent in the quadratic form?

In $ax^2 + bx + c$ , a is the coefficient of x², b is the coefficient of x, and c is the constant term with no variable.

Why is the fraction 1/2 kept as a fraction instead of converted to decimal?

Keeping $\frac{1}{2}$ as a fraction is more precise than 0.5 and shows the exact value. Fractions are preferred in algebraic expressions unless specifically asked for decimals.

Can I rearrange the terms in a different order?

Yes! $2x^2 + \frac{1}{2}x + 4$ equals $\frac{1}{2}x + 2x^2 + 4$ , but standard form puts the highest degree term first (x²), then x, then the constant.

What if one of the coefficients was zero?

If a coefficient is zero, that term disappears from the expression. For example, if b=0, you'd get $2x^2 + 4$ (no x term).

How do I check if my expression is correct?

Compare each part: the coefficient of x² should be a=2, the coefficient of x should be b=1/2, and the constant should be c=4.

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Formulate an Algebraic Expression with Constants: a=2, b=1/2, c=4

Quadratic Expressions 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 each letter represent in the quadratic form?

Why is the fraction 1/2 kept as a fraction instead of converted to decimal?

Can I rearrange the terms in a different order?

What if one of the coefficients was zero?

How do I check if my expression is correct?

🌟 Unlock Your Math Potential

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