Math Problem Statement
Convert -x^2+2x-6 into vertex form
Solution
To convert the quadratic equation into vertex form, we can complete the square. The vertex form of a quadratic equation is given by:
where is the vertex of the parabola.
Step 1: Factor out the coefficient of
Start by factoring out from the and terms.
Step 2: Complete the square
Take the coefficient of (which is ), divide it by 2, and square it.
Add and subtract 1 inside the parentheses to complete the square.
Step 3: Simplify the expression
Group the perfect square trinomial and simplify.
Distribute the .
Final Answer
The vertex form of is:
The vertex is .
Do you want any details or have any questions? Here are some related problems for further practice:
- Convert into vertex form.
- Find the vertex form of .
- Convert into vertex form.
- Find the vertex form of .
- Write in vertex form.
Tip: Always remember to factor out the coefficient of before completing the square.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Completing the Square
Formulas
Vertex form of a quadratic equation: y = a(x - h)^2 + k
Completing the square
Theorems
The process of completing the square to find the vertex form
Suitable Grade Level
Grades 9-11
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