Math Problem Statement
Solution
To write the quadratic function in vertex form, we need to complete the square.
Step 1: Start with the original equation.
Step 2: Complete the square.
- First, focus on the quadratic and linear terms: .
- To complete the square, take the coefficient of (which is ), divide by 2, and square it:
- Add and subtract this value inside the equation:
- Now, factor the perfect square trinomial:
- Combine the constant terms:
Final Answer in Vertex Form:
Matching to the Options:
The correct answer corresponds to Option D:
Would you like more details or have any questions?
Here are five related questions to expand your understanding:
- How do you find the vertex of a parabola from its vertex form?
- What is the significance of completing the square in quadratic equations?
- How would the process differ if the quadratic coefficient were not 1?
- Can the vertex form be used to determine the direction in which a parabola opens?
- How can you verify the vertex form by expanding it back to standard form?
Tip: Completing the square is not only useful for converting to vertex form but also plays a crucial role in solving quadratic equations and finding maximum or minimum values in calculus.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Vertex Form
Completing the Square
Formulas
Vertex form of a quadratic function: f(x) = a(x-h)^2 + k
Completing the square
Theorems
Properties of parabolas and their vertex
Suitable Grade Level
Grades 9-10
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