To provide the piecewise function and the vertex form, I would need a description or visual of the graph in question. However, I can explain how to extract this information if you have a particular graph in mind.
Piecewise Function:
- Identify Sections: Examine the graph and identify the different sections where the function behaves differently.
- Define Each Section: For each section, determine the corresponding rule (such as linear equations, quadratic equations, etc.).
- Write the Piecewise Function: Combine the rules using the piecewise notation.
For example: \[ f(x) = \begin{cases} \text{Rule 1} & \text{for } x < a \ \text{Rule 2} & \text{for } a \leq x < b \ \text{Rule 3} & \text{for } x \geq b \end{cases} \]
Vertex Form:
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.
For your question:
- What is the value of the first ? (h): This is the x-coordinate of the vertex.
- What is the value of the second ? (k): This is the y-coordinate of the vertex.
To find these values, look at the vertex location on your graph.
If you provide a description of the graph or its features (like its vertex, intercepts, etc.), I can help you more precisely with constructing the piecewise function or determining the vertex values.