Math Problem Statement
Solution
To convert the quadratic equation into vertex form, we need to complete the square.
Here's the step-by-step process:
1. Start with the given equation:
2. Factor out the constant term (which is ) for now, and focus on the quadratic and linear terms:
3. Complete the square:
To complete the square, take half of the coefficient of , which is 8, divide it by 2, and then square it:
Now, add and subtract 16 inside the parentheses:
4. Simplify the equation:
Now, simplify the constants:
Thus, the equation in vertex form is:
Answer:
The correct option is the first one:
Would you like further clarification on any part of the solution?
Here are 5 follow-up questions to deepen your understanding:
- How does completing the square help in converting to vertex form?
- What is the vertex of the parabola ?
- How do the values of and in vertex form affect the graph?
- Can you use another method to find the vertex without completing the square?
- How can you verify your solution by expanding the vertex form back into standard form?
Tip: Completing the square is an essential algebraic technique that helps in transforming quadratic equations into a more manageable form, revealing key properties like the vertex.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Completing the Square
Formulas
y = ax^2 + bx + c
Vertex form: y = a(x - h)^2 + k
Theorems
Vertex form of a quadratic equation
Suitable Grade Level
Grades 8-10
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