Formulate an Algebraic Expression: Use Parameters a=1, b=-1, c=3

Quadratic Expressions with Given Coefficients

Create an algebraic expression based on the following parameters:

a=1,b=1,c=3 a=1,b=-1,c=3

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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
00:20 We'll connect each parameter to its corresponding variable according to the formula
00:46 We'll write the function in its reduced form
01:04 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=1,c=3 a=1,b=-1,c=3

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the provided coefficients for the expression of the form ax2+bx+c ax^2 + bx + c .
  • Step 2: Substitute the provided values into the expression.

Now, let's perform these steps:

Step 1: The problem provides us with the coefficients a=1 a = 1 , b=1 b = -1 , and c=3 c = 3 for a quadratic expression ax2+bx+c ax^2 + bx + c .

Step 2: Substitute these values into the quadratic expression:

a=1 a = 1 : Multiply x2 x^2 by 1 1 , resulting in x2 x^2 .

b=1 b = -1 : Multiply x x by 1-1, resulting in x-x.

c=3 c = 3 : The constant term is 3 3 .

Thus, the algebraic expression is:

x2x+3 x^2 - x + 3 .

Comparing this result to the given choices, we find that this expression matches choice 3.

Therefore, the solution to the problem is x2x+3 x^2 - x + 3 .

3

Final Answer

x2x+3 x^2-x+3

Key Points to Remember

Essential concepts to master this topic
  • Standard Form: Quadratic expressions follow ax² + bx + c pattern
  • Substitution: Replace a=1, b=-1, c=3 to get 1x² + (-1)x + 3
  • Verification: Check coefficient order: x² term, x term, constant ✓

Common Mistakes

Avoid these frequent errors
  • Mixing up coefficient positions
    Don't put b=-1 in the constant position or c=3 with the x term = wrong expression! Each parameter has a specific position in ax² + bx + c. Always match a with x², b with x, and c as the constant term.

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 parameter represent in ax² + bx + c?

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a is the coefficient of x², b is the coefficient of x, and c is the constant term. They must stay in this exact order!

Why is b = -1 written as -x instead of +(-1)x?

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When the coefficient is negative, we simplify the expression. +(-1)x becomes -x for cleaner notation. Both mean the same thing mathematically.

What if a = 1? Do I still write 1x²?

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When the coefficient is 1, we typically don't write it. So 1x² becomes just x2 x^2 . This makes the expression cleaner and easier to read.

Can the parameters be fractions or decimals?

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Absolutely! The parameters a, b, and c can be any real numbers - positive, negative, fractions, or decimals. The substitution process works exactly the same way.

How do I know I built the expression correctly?

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Check that your expression has the form ax2+bx+c ax^2 + bx + c and verify each coefficient matches:

  • Coefficient of x² should equal a
  • Coefficient of x should equal b
  • Constant term should equal c

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