1. The problem is to analyze the function shown in the video link, which is $y = x^2 - 4x + 3$.\n\n2. The formula for a quadratic function is $y = ax^2 + bx + c$. Here, $a=1$, $b=-4$, and $c=3$.\n\n3. To find the roots (x-intercepts), use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$\n\n4. Calculate the discriminant: $$b^2 - 4ac = (-4)^2 - 4 \times 1 \times 3 = 16 - 12 = 4$$\n\n5. Substitute values into the quadratic formula: $$x = \frac{-(-4) \pm \sqrt{4}}{2 \times 1} = \frac{4 \pm 2}{2}$$\n\n6. Find the two roots: $$x_1 = \frac{4 + 2}{2} = 3, \quad x_2 = \frac{4 - 2}{2} = 1$$\n\n7. The vertex of the parabola is at $$x = -\frac{b}{2a} = -\frac{-4}{2 \times 1} = 2$$\n\n8. Find the y-coordinate of the vertex by substituting $x=2$: $$y = (2)^2 - 4(2) + 3 = 4 - 8 + 3 = -1$$\n\n9. The vertex is at $(2, -1)$, which is the minimum point since $a=1 > 0$.\n\n10. The y-intercept is found by evaluating $y$ at $x=0$: $$y = 0^2 - 4 \times 0 + 3 = 3$$\n\nFinal answer: The roots are $x=1$ and $x=3$, the vertex is at $(2, -1)$, and the y-intercept is $3$.