Here is the graph of the function \( f(x) = -2(x - 1)^2 + 2 \), showing its key points:

- The **vertex** is at \( (1, 2) \), marked at the top of the parabola.
- The **y-intercept** is at \( (0, 0) \).
- The function is symmetric about the **axis of symmetry** \( x = 1 \), indicated by the dashed green line.
- The parabola opens downward because the coefficient of \( (x - 1)^2 \) is negative, and it is vertically stretched due to the factor of -2.

Would you like more details or have any other questions?

Here are 5 related questions you could explore:
1. How does changing the value of \( a \) affect the width of the parabola?
2. What happens if the vertex of the parabola is moved to a different point?
3. How do you find the x-intercepts of a parabola, if they exist?
4. What role does symmetry play in the graph of a quadratic function?
5. How would the graph change if the equation were \( f(x) = 2(x - 1)^2 + 2 \)?

**Tip**: The vertex form of a quadratic equation provides an easy way to read the vertex and direction of the parabola directly from the equation.

f(x) = -2(x - 1)^2 + 2 graph and show work

Learn how to graph the quadratic function f(x) = -2(x - 1)^2 + 2 with step-by-step work. Explore key concepts such as the vertex form, symmetry, and the effect of coefficients on the shape of the parabola. Suitable for students in Grades 9-11.

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