Question
The graph shows the axis of symmetry for a quadratic function f(x).
On a coordinate plane, a vertical dashed line at (4, 0) is parallel to the y-axis.
Which could be the function?
f(x) = (x + 4)2
f(x) = x2 + 4
f(x) = (x – 4)2
f(x) = x2 – 4
On a coordinate plane, a vertical dashed line at (4, 0) is parallel to the y-axis.
Which could be the function?
f(x) = (x + 4)2
f(x) = x2 + 4
f(x) = (x – 4)2
f(x) = x2 – 4
Answers
GPT-4o mini
The axis of symmetry for a quadratic function in the standard form \( f(x) = a(x - h)^2 + k \) is the line \( x = h \), where \( (h, k) \) is the vertex of the parabola. Given that the axis of symmetry is at \( x = 4 \), we can determine the function by identifying which one matches this characteristic.
Let's analyze the options:
1. **\( f(x) = (x + 4)^2 \)**: The axis of symmetry is \( x = -4 \).
2. **\( f(x) = x^2 + 4 \)**: The axis of symmetry is \( x = 0 \).
3. **\( f(x) = (x - 4)^2 \)**: The axis of symmetry is \( x = 4 \).
4. **\( f(x) = x^2 - 4 \)**: The axis of symmetry is \( x = 0 \).
From the choices provided, the function that has an axis of symmetry at \( x = 4 \) is:
**\( f(x) = (x - 4)^2 \)**.
Let's analyze the options:
1. **\( f(x) = (x + 4)^2 \)**: The axis of symmetry is \( x = -4 \).
2. **\( f(x) = x^2 + 4 \)**: The axis of symmetry is \( x = 0 \).
3. **\( f(x) = (x - 4)^2 \)**: The axis of symmetry is \( x = 4 \).
4. **\( f(x) = x^2 - 4 \)**: The axis of symmetry is \( x = 0 \).
From the choices provided, the function that has an axis of symmetry at \( x = 4 \) is:
**\( f(x) = (x - 4)^2 \)**.