Math Problem Statement
Solution
The task in the image is to arrange the quadratic expressions in completed square form, corresponding to their respective original quadratic equations. The given quadratics are:
Their corresponding completed square forms are shown below the quadratics, but we need to match them correctly.
Let's complete the square for each expression:
1.
- Step 1: Half of the coefficient of is .
- Step 2: Square , which is 4.
- Step 3: Rewrite the expression: .
So the first expression corresponds to , which matches with iv in the boxed answers.
2.
- Step 1: Half of is .
- Step 2: Square , which is 9.
- Step 3: Rewrite .
So the second expression corresponds to , which matches with ii in the boxed answers.
3.
- Step 1: Factor out the 2 from the quadratic terms: .
- Step 2: Half of is , and squaring it gives 1.
- Step 3: Add and subtract 1 inside the parentheses: .
So the third expression corresponds to , which matches with i in the boxed answers.
4.
- Step 1: Factor out the 4: .
- Step 2: Half of is , and squaring it gives .
- Step 3: Rewrite: .
So the fourth expression corresponds to , which matches with iii in the boxed answers.
Final matching:
- iv
- ii
- i
- iii
Let me know if you need more details or further clarification! Here are five questions you can explore:
- How do you complete the square for a quadratic expression in general?
- What are the benefits of converting a quadratic expression into its completed square form?
- How does factoring affect the process of completing the square when dealing with quadratic expressions like ?
- Why is the completed square form useful for solving quadratic equations?
- How does completing the square help in finding the vertex of a parabola?
Tip: Completing the square is particularly useful when deriving the quadratic formula or finding the maximum/minimum values of a quadratic function.
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Math Problem Analysis
Mathematical Concepts
Completing the Square
Quadratic Expressions
Factoring
Formulas
Completing the square: ax^2 + bx + c = a(x-h)^2 + k
Quadratic expression
Theorems
Method of Completing the Square
Factoring Quadratics
Suitable Grade Level
Grades 9-12
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