Finding the vertex of a parabola is crucial for various mathematical applications. Here’s a quick and simple method:
Step-by-Step Guide
- Identify the parabolic equation in standard form: ( y = ax^2 + bx + c ).
- Use the formula: Vertex ((h, k) = left( -frac{b}{2a}, f(-frac{b}{2a}) right) ).
- Calculate ( h ): ( h = -frac{b}{2a} ).
- Substitute ( h ) back into the equation to find ( k ).
Example
| Equation | y = 2x² – 4x + 1 |
|---|---|
| h Value | (- frac{-4}{2*2} = 1) |
| k Value | y = 2(1)² – 4(1) + 1 = -1 |
| Vertex | (1, -1) |
Additional Resources
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