Math Problem Statement
vertex form of x^2+6x+2
Solution
To rewrite the quadratic equation in vertex form, we use the method of completing the square.
The vertex form of a quadratic equation is:
where is the vertex of the parabola.
Let's go through the steps:
1. Start with the original equation:
2. Isolate the quadratic and linear terms:
3. Complete the square:
To complete the square, take the coefficient of (which is 6), divide it by 2, and square it:
Now, add and subtract 9 inside the parentheses:
4. Simplify:
The expression inside the parentheses is now a perfect square:
Final answer:
The vertex form of the quadratic equation is:
This shows that the vertex is at .
Would you like a deeper explanation of any part of this process?
Here are 5 related questions to expand on this topic:
- How do you find the vertex from a quadratic equation in standard form?
- What does completing the square mean geometrically?
- How can the discriminant help in understanding the roots of a quadratic equation?
- How do you convert a quadratic equation to factored form?
- What is the significance of the axis of symmetry in a parabola?
Tip: When completing the square, always remember to balance the equation by adding and subtracting the same value!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Completing the Square
Vertex Form
Formulas
Vertex form: y = a(x - h)^2 + k
Completing the square: (b/2)^2
Theorems
Vertex form theorem
Completing the square method
Suitable Grade Level
Grades 8-10
Related Recommendation
Convert 2x^2 + 4x + 6 to Vertex Form Using Completing the Square
Rewriting Quadratic Equation y = –6x^2 + 3x + 2 into Vertex Form
Convert the Quadratic Equation -x^2 + 2x - 6 into Vertex Form
Convert Quadratic Equation -2x^2 + 14x + 6 into Vertex Form
Convert x^2 - 6x + 12 to Vertex Form Using Completing the Square