Math Problem Statement
How to translate vertex form to standard
Solution
To translate a quadratic equation from vertex form to standard form, follow these steps:
Vertex Form of a Quadratic Equation:
Where:
- is the same coefficient as in the standard form.
- is the vertex of the parabola.
Standard Form of a Quadratic Equation:
Where:
- , , and are constants.
Steps to Convert:
-
Expand the Square: Use the identity .
-
Distribute the :
-
Simplify:
Now, the equation is in standard form: Where:
Example:
Convert to standard form.
-
Expand:
-
Distribute :
-
Simplify:
This is the quadratic in standard form.
Would you like more examples or details on specific steps?
5 Follow-up Questions:
- How do you identify the vertex from the vertex form?
- What is the purpose of the coefficient in the vertex form?
- How can you find the axis of symmetry from the standard form?
- What happens when the vertex is at the origin?
- How does completing the square relate to converting from standard to vertex form?
Tip:
The value of remains the same when converting between vertex form and standard form—it dictates the direction and width of the parabola.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Vertex Form
Standard Form
Formulas
Vertex form: y = a(x - h)^2 + k
Standard form: y = ax^2 + bx + c
Expansion formula: (x - h)^2 = x^2 - 2hx + h^2
Theorems
Quadratic Expansion
Properties of Parabolas
Suitable Grade Level
Grades 9-12
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