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

Quadratic Expressions with Specific Parameters

Create an algebraic expression based on the following parameters:

a=1,b=2,c=0 a=-1,b=2,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 will use the formula to represent a quadratic equation
00:12 We will connect the parameter to the corresponding variable according to the formula
00:29 We will write the equation in reduced form
00:35 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=1,b=2,c=0 a=-1,b=2,c=0

2

Step-by-step solution

To formulate the quadratic expression using the given parameters, we follow these steps:

  • Step 1: Identify the formula: The standard form of a quadratic function is y=ax2+bx+c y = ax^2 + bx + c .
  • Step 2: Substitute the values: Insert a=1 a = -1 , b=2 b = 2 , and c=0 c = 0 into the formula.
  • Step 3: Simplify the expression: Apply the values directly and simplify where necessary.

Here’s how we perform each step:
Step 1: We start with the formula: y=ax2+bx+c y = ax^2 + bx + c .
Step 2: Substitute the given values: y=(1)x2+2x+0 y = (-1)x^2 + 2x + 0 .
Step 3: This simplifies to y=x2+2x y = -x^2 + 2x since adding zero does not change the expression.

Thus, the algebraic expression representing the quadratic function with the given parameters is y=x2+2x y = -x^2 + 2x .

3

Final Answer

x2+2x -x^2+2x

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=-1, b=2, c=0 to get x2+2x+0 -x^2 + 2x + 0
  • Simplification: Remove zero terms: x2+2x+0=x2+2x -x^2 + 2x + 0 = -x^2 + 2x

Common Mistakes

Avoid these frequent errors
  • Forgetting to apply the negative sign to the coefficient
    Don't write (-1)x² as just x² = wrong expression! The negative coefficient must be applied to create -x². Always carefully substitute each parameter value, especially negative ones.

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 systematic way to write any quadratic expression. The coefficients a, b, and c tell us about the shape, direction, and position of the parabola when graphed.

What happens when c = 0 like in this problem?

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When c = 0, the constant term disappears from the expression. This means the parabola passes through the origin (0,0) when graphed, since there's no vertical shift.

Does the order of terms matter in the final answer?

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The standard order is highest degree first: x² terms, then x terms, then constants. So x2+2x -x^2 + 2x is preferred over 2xx2 2x - x^2 .

How do I check if my substitution is correct?

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Double-check each coefficient: a=-1 goes with x², b=2 goes with x, c=0 is the constant. Then verify: (1)x2+(2)x+(0)=x2+2x (-1)x^2 + (2)x + (0) = -x^2 + 2x .

What if I accidentally wrote +x² instead of -x²?

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That's a common error! Remember that a = -1, so the x² term must be negative. Always pay extra attention to negative coefficients when substituting.

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