Use the method of completing the square to find the standard form of the quadratic function.

*f*(*x*) = −*x*2 + 4*x* + 2

*y* =

State the vertex and axis of symmetry of the graph of the function.

axis of symmetry

*x* =

vertex

(*x*, *y*) =

Sketch the graph.

The graph of the quadratic function \( y = - (x - 2)^2 + 6 \) is shown above. It clearly displays the parabola opening downwards, with the vertex at \((2, 6)\) and the axis of symmetry as a dashed vertical line at \(x = 2\).

### Summary
- **Standard Form:** \( y = - (x - 2)^2 + 6 \)
- **Vertex:** \((2, 6)\)
- **Axis of symmetry:** \( x = 2 \)

Would you like more details or have any questions?

### Related Questions
1. How can you determine whether a parabola opens upward or downward?
2. What is the significance of the vertex in a quadratic function's graph?
3. How do you convert from the vertex form back to the standard form of a quadratic equation?
4. How does changing the coefficient of \(x^2\) affect the shape of the parabola?
5. What are the steps to find the x-intercepts and y-intercepts of a quadratic function?

### Tip
Completing the square is a powerful technique to transform any quadratic equation into its vertex form, making it easier to identify key features like the vertex and axis of symmetry.

Use the method of completing the square to find the standard form of the quadratic function.
f(x) = −x^2 + 4x + 2
y = 
State the vertex and axis of symmetry of the graph of the function.
Axis of symmetry: x = 
Vertex: (x, y) = 
Sketch the graph.

Learn how to complete the square to find the standard (vertex) form of the quadratic function f(x) = -x^2 + 4x + 2. This step-by-step solution includes finding the vertex at (2, 6) and the axis of symmetry at x = 2. Suitable for students in Grades 9-12.

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