How do you identify the vertex, the axis of symmetry, max or min value, and the domain and range or a function?
y=-1.5(x+20)^2
from the standard version of this form,
vertex is (-20,0)
axis of symmetry: x -20
min is 0
domain: any real number
range: any real number, y≥0
To identify the vertex, axis of symmetry, maximum or minimum value, domain, and range of a function, you can use the standard form of a quadratic function, which is expressed as y = a(x - h)^2 + k. In this case, you are given the equation y = -1.5(x + 20)^2.
1. Vertex: In the standard form, the vertex of a quadratic function is given by the coordinate (h, k). So, for the given function, the vertex will be the point (-20, 0), since (h, k) corresponds to (-20, 0).
2. Axis of Symmetry: The axis of symmetry is a vertical line that passes through the vertex of a quadratic function. The equation of the axis of symmetry is x = h, where h is the x-coordinate of the vertex. Therefore, for the given function, the axis of symmetry will be x = -20.
3. Maximum or Minimum Value: For a quadratic function in standard form, the vertex represents either the maximum or minimum value depending on the coefficient 'a'. If 'a' is positive, the parabola opens upward, and the vertex represents the minimum value. Conversely, if 'a' is negative, the parabola opens downward, and the vertex represents the maximum value. In this case, 'a' is -1.5, so the parabola opens downward, and the vertex (0) represents the maximum value.
4. Domain: The domain of a function is the set of all possible x-values for which the function is defined. Since a quadratic function is defined for all real numbers, the domain is (-∞, +∞) or all real numbers.
5. Range: The range is the set of all possible y-values that the function can take. For the given function, since 'a' is negative, the parabola opens downward, and the range will be (-∞, k], where k represents the y-coordinate of the vertex. In this case, since the vertex is (0), the range will be (-∞, 0].