: Sketch, on the same coordinate plane, the
graphs of ffor the given values of c. (Make use of symmetry,
shifting, stretching, compressing, or reflecting.)
f共x兲 		1
2 共x 	 c兲2
c= -3,0,4

Here is the graph of the function \( f(x) = \frac{1}{2}(x - c)^2 \) for three different values of \( c \): \( c = -3 \), \( c = 0 \), and \( c = 4 \).

- The **blue curve** corresponds to \( c = -3 \), which shifts the parabola 3 units to the left.
- The **green curve** corresponds to \( c = 0 \), which is the standard parabola centered at the origin.
- The **red curve** corresponds to \( c = 4 \), which shifts the parabola 4 units to the right.

Each parabola is vertically compressed (wider) due to the factor \( \frac{1}{2} \).

If you have any questions or would like further details, feel free to ask!

### Relative questions:
1. How does changing the value of \( c \) affect the graph of the function?
2. What role does the \( \frac{1}{2} \) coefficient play in the shape of the parabola?
3. What would happen to the graph if the coefficient were negative instead of positive?
4. Can you describe the vertex form of a parabola and its importance?
5. How would the graph change if the exponent on \( (x - c) \) were different?

### Tip:
To quickly graph parabolas, remember that the vertex form \( f(x) = a(x - h)^2 + k \) reveals the vertex at \( (h, k) \) and determines the width based on \( a \).

Explore how to graph quadratic functions of the form f(x) = (1/2)(x - c)^2 for different values of c. Understand how each value of c affects the position and shape of the parabola. Suitable for high school students studying functions and transformations.

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