Assignment Sketch a graph of f . $$ f(x)=4 x^{2} $$

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To sketch the graph of the function $$ f(x) = 4x^2 $$, we can follow these steps:

1. **Identify the type of function**: The function $$ f(x) = 4x^2 $$ is a quadratic function, which means its graph will be a parabola.

2. **Determine the vertex**: The vertex of the parabola represented by $$ f(x) = ax^2 + bx + c $$ is at the point $$ (0, 0) $$ since there are no linear or constant terms (i.e., $$ b = 0 $$ and $$ c = 0 $$).

3. **Determine the direction of the parabola**: Since the coefficient of $$ x^2 $$ (which is 4) is positive, the parabola opens upwards.

4. **Calculate some key points**: We can calculate the values of $$ f(x) $$ for several values of $$ x $$:
   - $$ f(-2) = 4(-2)^2 = 16 $$
   - $$ f(-1) = 4(-1)^2 = 4 $$
   - $$ f(0) = 4(0)^2 = 0 $$
   - $$ f(1) = 4(1)^2 = 4 $$
   - $$ f(2) = 4(2)^2 = 16 $$

5. **Plot the points**: The points we have calculated are:
   - $$ (-2, 16) $$
   - $$ (-1, 4) $$
   - $$ (0, 0) $$
   - $$ (1, 4) $$
   - $$ (2, 16) $$

6. **Draw the graph**: Connect these points with a smooth curve to form the parabola.

### Summary of the Graph
- The vertex is at $$ (0, 0) $$.
- The parabola opens upwards.
- The graph is symmetric about the y-axis.

You can sketch this on graph paper or using graphing software by plotting the points and drawing the curve through them.
To sketch the graph of $$ f(x) = 4x^2 $$, plot the vertex at (0,0), draw a symmetric parabola opening upwards, and plot key points like (-2,16), (-1,4), (0,0), (1,4), and (2,16). Connect these points with a smooth curve to form the parabola.

Assignment Sketch a graph of f . \( f(x)=4 x^{2} \)

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