The vertex is at (9, 0).
Identify the axis of symmetry.
The axis of symmetry is the vertical line that passes through the vertex. Therefore, the axis of symmetry is the vertical line x = 9.
Identify the maximum or minimum value.
Since the leading coefficient is negative, the parabola opens downwards and the vertex represents the maximum point of the function. Therefore, the maximum value is f(9) = 0.
Identify the domain and range of the function.
The domain is all real numbers, since there are no restrictions on the values of x that can be inputted into the function. The range, however, is bounded by the vertex, since the maximum value is at the vertex. Therefore, the range is (-∞, 0].
Identify the vertex, the axis of symmetry, the maximum or minimum value, and the domain and range of function
f(x) = -(x-9)^2
Identify the vertex.
the coordinates of the vertex are
(the an ordered pair)
3 answers
its (9, -20)
If the coordinates of the vertex are (9, -20), then we have:
- Vertex: (9, -20)
- Axis of symmetry: x = 9
- Maximum or minimum value: Since the leading coefficient is negative, the parabola opens downwards and the vertex represents the maximum point of the function. Therefore, the maximum value is f(9) = -20.
- Domain: All real numbers
- Range: The range is bounded by the vertex, since the maximum value is at the vertex. Therefore, the range is (-∞, -20].
- Vertex: (9, -20)
- Axis of symmetry: x = 9
- Maximum or minimum value: Since the leading coefficient is negative, the parabola opens downwards and the vertex represents the maximum point of the function. Therefore, the maximum value is f(9) = -20.
- Domain: All real numbers
- Range: The range is bounded by the vertex, since the maximum value is at the vertex. Therefore, the range is (-∞, -20].
1 answer