Match the equation, graph, key features, and the transformation on the parent function to the table of values of each function.

To best assist you, I’ll need a bit more context about the specific equations, graphs, key features, and transformations you have available. However, I can provide an example of how you might match these elements if you were given a set of common functions.

Example:

Equations:

1. \( y = x^2 \)
2. \( y = (x - 3)^2 + 1 \)
3. \( y = -2(x + 1)^2 + 4 \)

Graphs: (You would usually present images of the graphs for these functions.)

Key Features:

• \( y = x^2 \):

  • Vertex at (0,0)
  • Opens upwards
  • Symmetrical about the y-axis

• \( y = (x - 3)^2 + 1 \):

  • Vertex at (3,1)
  • Opens upwards
  • Shifted right 3 units and up 1 unit from the parent function

• \( y = -2(x + 1)^2 + 4 \):

  • Vertex at (-1,4)
  • Opens downwards
  • Reflected over the x-axis, vertically stretched by a factor of 2, and shifted left 1 unit and up 4 units

Transformations:

• Parent function \( y = x^2 \):
  • No transformation
• Transformed to create \( y = (x - 3)^2 + 1 \):
  • Right 3, Up 1
• Transformed to create \( y = -2(x + 1)^2 + 4 \):
  • Left 1, Up 4, Reflect over x-axis, Vertically stretch by 2

Matching Table:

| Equation | Graph | Key Features | Transformation | |---------------------------------------------------|-------------------------|-------------------------------------------|-----------------------------------------------------| | \( y = x^2 \) | (Graph of parabola) | Vertex at (0,0), Opens upwards | No transformation | | \( y = (x - 3)^2 + 1 \) | (Graph of upward shift) | Vertex at (3,1), opens upwards | Right 3, Up 1 | | \( y = -2(x + 1)^2 + 4 \) | (Graph of downward shift) | Vertex at (-1,4), opens downwards | Left 1, Up 4, Reflect over x-axis, Vertically stretch by 2 |

If you provide the specific functions and features you have, I can create a more tailored response!