Graph the quadratic function below. \( y=2 x^{2}-4 x+4 \)

To graph the quadratic function \( y=2x^{2}-4x+4 \), we can start by identifying the vertex of the parabola. The vertex form of a quadratic function is given by \( y=a(x-h)^{2}+k \), where \( (h,k) \) is the vertex of the parabola. To find the vertex, we can complete the square on the quadratic function. Given function: \( y=2x^{2}-4x+4 \) Completing the square: \( y=2(x^{2}-2x)+4 \) \( y=2(x^{2}-2x+1)+4-2 \) \( y=2(x-1)^{2}+2 \) Therefore, the vertex of the parabola is at \( (1,2) \). Now, we can plot the vertex and use it to determine the direction of the parabola. Since the coefficient of \( x^{2} \) is positive, the parabola opens upwards. To graph the function, we can plot the vertex and then use the symmetry of the parabola to plot the other points. The parabola is symmetric about the vertical line passing through the vertex. Let's plot the vertex and some additional points to visualize the graph.