Final answer:
The domain of the function is all real numbers, the range is y , the vertex is (−2, 3), and the axis of symmetry is x = −2.
Step-by-step explanation:
a) Domain of the function: The domain of the function is the set of all possible x-values for which the function is defined. In this case, there are no restrictions on the x-values, so the domain is all real numbers.
b) Range of the function: The range of the function is the set of all possible y-values that the function can take. Since the function is a downward-facing parabola and the coefficient of the quadratic term is negative, the maximum value of the function occurs at the vertex, which is the y-coordinate of the parabola. In this case, the vertex is (−2,3), so the range of the function is y .
c) Vertex of the function: The vertex of the function can be found by using the formula (h, k), where h is the x-coordinate and k is the y-coordinate. In this case, the x-coordinate of the vertex is −2, and the y-coordinate is 3. Therefore, the vertex of the function is (−2, 3).
d) Axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex of the parabola. In this case, the axis of symmetry is the vertical line x = −2.