Write the quadratic function in the form \( y=a(x-h)^{2}+k \) and sketch its graph. \( y=x^{2}-4 x \)

To convert y = x² - 4x into vertex form (y = a(x - h)² + k), follow these steps: 1. Start with the function:   y = x² - 4x 2. Factor out the coefficient of x² (in this case, it’s 1, so nothing changes):   y = x² - 4x 3. Complete the square:   • Take half the coefficient of x: ½(-4) = -2.   • Square it: (-2)² = 4.   • Add and subtract 4 inside the expression:     y = (x² - 4x + 4) - 4 4. Now write the quadratic as a perfect square:   y = (x - 2)² - 4 Thus, the vertex form is:   y = (x - 2)² - 4 Graph Details:  • Vertex: The vertex (h, k) is (2, -4).  • Axis of Symmetry: x = 2.  • x-intercepts: Set y = 0 in the original equation:   x² - 4x = 0 ⟹ x(x - 4) = 0 ⟹ x = 0 or x = 4.  • y-intercept: Set x = 0:   y = 0² - 4(0) = 0, so the point is (0, 0). Sketch Instructions:  1. Plot the vertex at (2, -4).  2. Draw the axis of symmetry, a vertical line through x = 2.  3. Mark the x-intercepts at (0, 0) and (4, 0) and the y-intercept at (0, 0).  4. Draw a smooth U-shaped (upward opening) curve passing through these points. This graph represents the parabola y = (x - 2)² - 4.