Question
1. The figure below shows a graph of the function of f(x) in the coordinate plane.
(6 points)
Part A:
Identify the following key features of the graph:
A. Vertex: (
,
)
B. Axis of symmetry : x=
C. y-intercept: (0,
)
C. x-intercepts from left to right: (
, 0) and (
, 0).
Question 2
Part B:
(6 points)
Part A:
Identify the following key features of the graph:
A. Vertex: (
,
)
B. Axis of symmetry : x=
C. y-intercept: (0,
)
C. x-intercepts from left to right: (
, 0) and (
, 0).
Question 2
Part B:
Answers
GPT-4o mini
It appears that you are referring to a specific graph of a function \( f(x) \) that is not visible in the text. To accurately identify the key features of the graph, I would need either a description of the graph or the graph itself.
However, I can explain how to determine the key features of a quadratic function, as they often appear in graph problems. Here’s a brief overview of how to find the vertex, axis of symmetry, y-intercept, and x-intercepts of a quadratic graph in general:
### Part A: Key Features of the Graph
1. **Vertex**:
- For a quadratic function in standard form \( f(x) = ax^2 + bx + c \), the vertex can be found using the formula:
\[
x = -\frac{b}{2a}
\]
- Once you find \( x \), substitute it back into the function to find \( f(x) \), which gives the vertex coordinates \((x, f(x))\).
2. **Axis of Symmetry**:
- The axis of symmetry is the vertical line that passes through the vertex, which can be represented as:
\[
x = -\frac{b}{2a}
\]
3. **y-intercept**:
- The y-intercept occurs where \( x = 0 \). To find it, calculate \( f(0) \). The coordinates of the y-intercept will be \((0, f(0))\).
4. **x-intercepts**:
- The x-intercepts can be found by solving the equation \( f(x) = 0 \). Graphically, these are the points where the graph crosses the x-axis, and their coordinates will be \((x_1, 0)\) and \((x_2, 0)\).
### Part B:
If you have specific elements of the graph or a description, please provide that information, and I can assist you further with calculating the values mentioned.
However, I can explain how to determine the key features of a quadratic function, as they often appear in graph problems. Here’s a brief overview of how to find the vertex, axis of symmetry, y-intercept, and x-intercepts of a quadratic graph in general:
### Part A: Key Features of the Graph
1. **Vertex**:
- For a quadratic function in standard form \( f(x) = ax^2 + bx + c \), the vertex can be found using the formula:
\[
x = -\frac{b}{2a}
\]
- Once you find \( x \), substitute it back into the function to find \( f(x) \), which gives the vertex coordinates \((x, f(x))\).
2. **Axis of Symmetry**:
- The axis of symmetry is the vertical line that passes through the vertex, which can be represented as:
\[
x = -\frac{b}{2a}
\]
3. **y-intercept**:
- The y-intercept occurs where \( x = 0 \). To find it, calculate \( f(0) \). The coordinates of the y-intercept will be \((0, f(0))\).
4. **x-intercepts**:
- The x-intercepts can be found by solving the equation \( f(x) = 0 \). Graphically, these are the points where the graph crosses the x-axis, and their coordinates will be \((x_1, 0)\) and \((x_2, 0)\).
### Part B:
If you have specific elements of the graph or a description, please provide that information, and I can assist you further with calculating the values mentioned.