The Algebraic Expression Challenge: Formulate Using a=3, b=6, c=9

Quadratic Expressions with Standard Form

Create an algebraic expression based on the following parameters:

a=3,b=6,c=9 a=3,b=6,c=9

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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.
00:11 We'll use the formula to represent a quadratic equation, step by step.
00:19 Match each parameter with the right variable, as shown in the formula.
00:39 And that's how we find the solution to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Create an algebraic expression based on the following parameters:

a=3,b=6,c=9 a=3,b=6,c=9

2

Step-by-step solution

To solve this problem, we will follow these steps:

  • Step 1: Identify the given parameters a=3 a = 3 , b=6 b = 6 , c=9 c = 9 .
  • Step 2: Use the standard formula for a quadratic expression, which is y=ax2+bx+c y = ax^2 + bx + c .
  • Step 3: Substitute the given values into this formula.

Now, let's work through each step:
Step 1: We have the parameters a=3 a = 3 , b=6 b = 6 , c=9 c = 9 .
Step 2: The standard form of a quadratic equation is y=ax2+bx+c y = ax^2 + bx + c .
Step 3: Substituting the given values into the expression, we get:

y=3x2+6x+9 y = 3x^2 + 6x + 9

Therefore, the algebraic expression based on the given parameters is:

3x2+6x+9 3x^2 + 6x + 9 .

3

Final Answer

3x2+6x+9 3x^2+6x+9

Key Points to Remember

Essential concepts to master this topic
  • Formula: Standard quadratic form is ax2+bx+c ax^2 + bx + c
  • Substitution: Replace a=3, b=6, c=9 to get 3x2+6x+9 3x^2 + 6x + 9
  • Verify: Check coefficients match given values: 3, 6, 9 ✓

Common Mistakes

Avoid these frequent errors
  • Switching coefficient positions or signs
    Don't write 6x2+3x+9 6x^2 + 3x + 9 or 3x26x+9 3x^2 - 6x + 9 = wrong expression! This changes the mathematical relationship completely. Always place coefficients in exact order: a with x², b with x, c as constant.

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 'standard form' mean for quadratic expressions?

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Standard form means writing the expression as ax2+bx+c ax^2 + bx + c where a, b, and c are specific numbers. The x² term comes first, then x term, then the constant.

Do I always need to include all three terms?

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Yes! Even if a coefficient is given, you must include its corresponding term. With a=3, b=6, c=9, you need all three parts: the x² term, x term, and constant term.

What if one of the coefficients was zero?

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If a coefficient is zero, that term disappears from the expression. For example, if b=0, you'd get 3x2+9 3x^2 + 9 . But in this problem, all coefficients are non-zero.

Can I rearrange the terms in a different order?

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No! Standard form has a specific order: x² term first, then x term, then constant. This order makes it easy to identify the coefficients and work with the expression.

How do I remember which coefficient goes where?

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Think alphabetically: a goes with x², b goes with x, c is the constant (no variable). Follow the pattern: ax2+bx+c ax^2 + bx + c .

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