Step-by-step explanation:
From the given equations of the function,
1). f(x) = x² + 4x + 3
     = x² + 2(2x) + 4 - 1
  f(x) = (x + 2)² - 1
  This is in the vertex form of a parabola [y = (x - h)² + k]
  Here, (h, k) is the vertex of the parabola.
  By comparing both the equations of the parabola,
  (-2, 1) will be the vertex.
  Table for input - output values,
  x intercepts → (x + 2)² + 1 = 0
              (x + 2) = ±1
              x = -2 ± 1
              x = -3, -1
  Line of symmetry → x = -3
  y-intercept of the graph, x = 0
              y = (0 + 2)²- 1
                = 4 - 1
              y = 3
2). f(x) = x² - 6x + 11
     = x² - 2(3x) + 9 + 2
     = (x - 3)² + 2
   By comparing the equation of the function with the vertex form of the parabola,
  (3, -2) is the vertex.
   Line of symmetry → x = 3
   x-intercept → (x - 3)² + 2 = 0
              (x - 3) = ±√(-2)
               x = 3 ± √(-2)  [Imaginary number]
   Therefore, NO y-intercept.
   y-intercept → y = 0 - 6(0) + 11 = 11    Â
3). f(x) = -x² + 2x - 2
     = -[x² - 2x + 2]
     = -[x² - 2(1.x) + 1 - 1] - 2
     = -[(x - 1)²- 1] - 2
     = -(x - 1)²- 1
By comparing this equation with the vertex form of the equation,
(1, -1) is the vertex. Â
x - intercepts → y = -(x - 1)²- 1 = 0
             (x - 1) = ±√(-1)
             x = 1 ± √(-1) [Imaginary numbers]
Therefore, no x-intercepts.
y-intercept → y = -(0 - 1)² + 3
           y = 2
4). y =
  y =
  y =
  y =
  y =
  y =
  Vertex → (4, -3)
  Line of symmetry → x = 4
  x - intercepts → x = 4 ± √6
               x = 1.55, 6.45
  y - intercepts → y = 5