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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

1 answer

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.