Question
What is the domain of the function in the graph?
A parabola has vertex at (0, 4), intercept x-axis at (-2, 0), and (2, 0).
A.-2≤ x ≤2
B. B.0≤x≤2
C.
x is all real numbers less than or equal to 4
D.
x is all real numbers
A parabola has vertex at (0, 4), intercept x-axis at (-2, 0), and (2, 0).
A.-2≤ x ≤2
B. B.0≤x≤2
C.
x is all real numbers less than or equal to 4
D.
x is all real numbers
Answers
GPT-4o mini
To determine the domain of the function represented by the parabola with the given vertex at (0, 4) and x-intercepts at (-2, 0) and (2, 0), we need to consider the x-values that the parabola covers.
1. The vertex at (0, 4) indicates that the highest point of the parabola is at x = 0.
2. The x-intercepts (-2, 0) and (2, 0) indicate where the parabola intersects the x-axis.
Since the parabola opens downwards (as the vertex is above the x-axis), it spans all x-values from the leftmost intercept (-2) to the rightmost intercept (2). Therefore, the x-values of the parabola range from -2 to 2, inclusive.
This means the domain of the function is:
**A. -2 ≤ x ≤ 2**
So, the correct answer is **A. -2 ≤ x ≤ 2**.
1. The vertex at (0, 4) indicates that the highest point of the parabola is at x = 0.
2. The x-intercepts (-2, 0) and (2, 0) indicate where the parabola intersects the x-axis.
Since the parabola opens downwards (as the vertex is above the x-axis), it spans all x-values from the leftmost intercept (-2) to the rightmost intercept (2). Therefore, the x-values of the parabola range from -2 to 2, inclusive.
This means the domain of the function is:
**A. -2 ≤ x ≤ 2**
So, the correct answer is **A. -2 ≤ x ≤ 2**.