Specific Algebra Task: Create an Expression with a = -3, b = 15, c = 0

Quadratic Expressions with Zero Constant Terms

Create an algebraic expression based on the following parameters:

a=3,b=15,c=0 a=-3,b=15,c=0

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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
00:11 We'll connect each parameter to its corresponding variable according to the formula
00:31 We'll write the function in its reduced form
00:37 And this is the solution to the 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=15,c=0 a=-3,b=15,c=0

2

Step-by-step solution

To solve this problem, we will follow these steps:

  • Step 1: Substitute the given values a=3 a = -3 , b=15 b = 15 , and c=0 c = 0 into the quadratic formula ax2+bx+c ax^2 + bx + c .
  • Step 2: Simplify the expression, removing any terms where the coefficient is zero.

Let's apply these steps:

Step 1: Start with the standard form of a quadratic expression ax2+bx+c ax^2 + bx + c . Given a=3 a = -3 , b=15 b = 15 , and c=0 c = 0 , substitute these values:

y=3x2+15x+0 y = -3x^2 + 15x + 0

Step 2: Simplify the expression:

The term +0 +0 can be removed because it does not affect the value of the expression, leading to:

y=3x2+15x y = -3x^2 + 15x

Thus, the algebraic expression based on the parameters provided is 3x2+15x -3x^2 + 15x .

Among the given choices, the correct choice is:

  • Choice 4: 3x2+15x -3x^2 + 15x
3

Final Answer

3x2+15x -3x^2+15x

Key Points to Remember

Essential concepts to master this topic
  • Standard Form: Quadratic expressions follow the pattern ax2+bx+c ax^2 + bx + c
  • Substitution: Replace coefficients: a = -3, b = 15, c = 0 gives 3x2+15x+0 -3x^2 + 15x + 0
  • Simplify: Remove zero terms: 3x2+15x+0=3x2+15x -3x^2 + 15x + 0 = -3x^2 + 15x

Common Mistakes

Avoid these frequent errors
  • Forgetting to remove zero terms or changing coefficient signs
    Don't write 3x2+15x+0 -3x^2 + 15x + 0 as your final answer = unnecessary complexity! The +0 adds nothing to the expression. Always simplify by removing zero terms to get the cleanest form: 3x2+15x -3x^2 + 15x .

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

Why do we use the standard form ax² + bx + c?

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The standard form gives us a consistent way to organize quadratic expressions. The coefficients a, b, and c tell us important information about the parabola's shape and position.

What happens when c = 0 like in this problem?

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When c = 0, there's no constant term! This means the parabola passes through the origin (0,0). You can simply leave out the +0 part in your final expression.

Do I always need to write the terms in x², x, constant order?

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Yes! Standard form requires this specific order. It makes expressions easier to read and compare. Always write highest degree term first: ax2+bx+c ax^2 + bx + c .

What if one of the coefficients is negative?

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Keep the negative sign with its coefficient! In our example, a = -3 stays as 3x2 -3x^2 . Don't change it to 3x2 3x^2 or you'll have the wrong expression.

How do I know which answer choice is correct?

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Compare your simplified expression to each choice carefully. Look for the exact same coefficients and make sure no unnecessary terms (like +0) are included in the final answer.

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