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

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.