Developing an Algebraic Expression: Substitute Values a=-10, b=2, c=0

Quadratic Expressions with Zero Constants

Create an algebraic expression based on the following parameters:

a=10,b=2,c=0 a=-10,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 Connect the parameter to the corresponding variable according to the formula
00:30 Write the function in its simplified form
00:39 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=10,b=2,c=0 a=-10,b=2,c=0

2

Step-by-step solution

To solve this problem, we will create an algebraic expression by following these steps:

  • Step 1: Identify the standard form of a quadratic function, y=ax2+bx+c y = ax^2 + bx + c .
  • Step 2: Substitute the given values a=10 a = -10 , b=2 b = 2 , and c=0 c = 0 into the formula.
  • Step 3: Simplify the resulting expression.

Let's apply these steps:

Step 1: The standard quadratic function format is given as y=ax2+bx+c y = ax^2 + bx + c .

Step 2: Substitute the given values:

y=(10)x2+2x+0 y = (-10)x^2 + 2x + 0

Step 3: Simplify the expression by removing the zero term (as c=0 c = 0 and it has no impact on the expression):

y=10x2+2x y = -10x^2 + 2x

This simplified expression y=10x2+2x y = -10x^2 + 2x is the required algebraic representation based on the given parameters.

Therefore, the correct algebraic expression for the parameters a=10 a = -10 , b=2 b = 2 , and c=0 c = 0 is 10x2+2x\boxed{-10x^2 + 2x}.

3

Final Answer

10x2+2x -10x^2+2x

Key Points to Remember

Essential concepts to master this topic
  • Standard Form: Quadratic expressions follow ax² + bx + c format
  • Substitution: Replace a=-10, b=2, c=0 to get -10x² + 2x + 0
  • Simplify: Remove zero terms: -10x² + 2x + 0 = -10x² + 2x ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to include negative signs when substituting
    Don't write 10x² instead of -10x² when a=-10 = wrong expression! The negative sign is part of the coefficient value. Always include the sign when substituting: a=-10 means the x² term becomes -10x².

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 remove the +0 at the end?

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Adding zero to any expression doesn't change its value. So 10x2+2x+0 -10x^2 + 2x + 0 simplifies to 10x2+2x -10x^2 + 2x for a cleaner final answer.

What if c wasn't zero?

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Then you'd keep the constant term! For example, if c=5, your expression would be 10x2+2x+5 -10x^2 + 2x + 5 . Only remove terms that equal zero.

Does the order of terms matter?

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Mathematically no, but standard form arranges terms by decreasing powers: x² term first, then x term, then constant. This makes expressions easier to read and compare.

How do I know which coefficient goes with which term?

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In ax2+bx+c ax^2 + bx + c :

  • a is the coefficient of x²
  • b is the coefficient of x
  • c is the constant term

What does it mean that a is negative?

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A negative coefficient for x² means the parabola opens downward when graphed. The negative sign is crucial - don't drop it during substitution!

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