Create an Algebraic Expression with Given Parameters: a=4, b=2, c=5

Q: What does each coefficient represent in a quadratic expression?

In $ ax^2 + bx + c $:a = coefficient of x² (the quadratic term)b = coefficient of x (the linear term)c = constant term (no variable)

Q: Why is the order of coefficients so important?

The order determines the degree of each term! Switching a=4 and b=2 would give you $ 2x^2 + 4x + 5 $, which is a completely different quadratic expression with different properties.

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

Mathematically yes, but standard form is always written in descending order of powers: x² term first, then x term, then constant. This makes expressions easier to read and compare.

Quadratic Expressions with Given Coefficients

Create an algebraic expression based on the following parameters:

$a=4,b=2,c=5$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's convert the parameters into a quadratic function.

00:12 We'll use the formula to write a quadratic equation.

00:16 Connect each parameter to its corresponding variable as per the formula.

00:36 And there we have it. That's our solution to the problem.

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:

$a=4,b=2,c=5$

Step-by-step solution

To derive the algebraic expression based on the parameters given, we follow these steps:

Step 1: Recognize the given parameters: $a = 4$ , $b = 2$ , and $c = 5$ .
Step 2: Acknowledge that the standard form for a quadratic expression is $y = ax^2 + bx + c$ .
Step 3: Substitute the given parameter values into this quadratic expression.

Now, let's implement these steps to form the quadratic expression:
Step 1: The given parameters are $a = 4$ , $b = 2$ , and $c = 5$ .
Step 2: Our basis is the quadratic form $y = ax^2 + bx + c$ .
Step 3: Substituting the given values, we find:

$y = 4x^2 + 2x + 5$

This substitution provides us with the quadratic expression $y = 4x^2 + 2x + 5$ , fulfilling the problem's requirements.

Therefore, the correct algebraic expression is $4x^2 + 2x + 5$ .

Final Answer

$4x^2+2x+5$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic expressions follow the pattern $ax^2 + bx + c$
Substitution: Replace a=4, b=2, c=5 to get $4x^2 + 2x + 5$
Verification: Check coefficients match given parameters: a=4, b=2, c=5 ✓

Common Mistakes

Avoid these frequent errors

Mixing up coefficient order or positions
Don't place coefficients randomly like putting b=2 with x² term = $2x^2 + 4x + 5$ ! This changes the entire expression structure and gives wrong answers. Always match coefficients to their correct positions: a goes with x², b 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 each coefficient represent in a quadratic expression?

In $ax^2 + bx + c$ :

a = coefficient of x² (the quadratic term)
b = coefficient of x (the linear term)
c = constant term (no variable)

Why is the order of coefficients so important?

The order determines the degree of each term! Switching a=4 and b=2 would give you $2x^2 + 4x + 5$ , which is a completely different quadratic expression with different properties.

What if one of the coefficients is negative?

Just substitute the negative value directly! For example, if a=-3, b=2, c=1, you'd get $-3x^2 + 2x + 1$ . The negative sign becomes part of the coefficient.

Can I write the terms in a different order?

Mathematically yes, but standard form is always written in descending order of powers: x² term first, then x term, then constant. This makes expressions easier to read and compare.

What happens if a coefficient is zero?

If a=0, you don't have a quadratic anymore - it becomes linear! If b=0, you skip the x term. If c=0, there's no constant term. For example: a=4, b=0, c=5 gives $4x^2 + 5$ .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 The Quadratic Function questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Create an Algebraic Expression with Given Parameters: a=4, b=2, c=5

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 coefficient represent in a quadratic expression?

Why is the order of coefficients so important?

What if one of the coefficients is negative?

Can I write the terms in a different order?

What happens if a coefficient is zero?

🌟 Unlock Your Math Potential

More Questions

The function y=ax²+bx+c

Craft an Algebraic Expression Using Parameters: a = -1, b = 1, c = 2

Parameter Challenge: Find the Representation for a=-3, b=4, c=-15

Constructing an Algebraic Expression with a=2, b=0, c=0

Craft an Algebraic Expression with Given Constants: a=5, b=3, c=-4

Standard Representation

Create an Algebraic Expression with Parameters: a=2, b=2, c=2

Create an Algebraic Expression Using Parameters: a = -1, b = -2, c = -5

Construct an Algebraic Expression Using a=1, b=1, c=0

Create an Algebraic Expression Using a = 1/2, b = 1/2, c = 1/2

Plotting Functions with Parameters

Create an Algebraic Expression with Variables a=4, b=-2, c=16

Construct an Algebraic Expression with Constants: a = -2, c = 3, 4

Crafting an Algebraic Expression: Using a=4, b=0, c=2

Create an Algebraic Expression: Using Parameters a=1, b=2, c=0