Is knowing the coordinates of the vertex of a parabola enough to determine the domain and range?

a. no: we would have no information about the domain.
b. yes: if the vertex is at (m, n), then the domain is all reals and the range is y ≤ n.
c. no: we would need to know if the vertex is a minimum or a maximum.
d. yes: if the vertex is at (m, n), then the domain is all reals and the range is y ≥ n.

use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following equation.

y=2x-x+6

a)( 0.25, 6.125)
.25, 5.875)
c)( 0.25, 5.875)
d)( 0.25, 6)

The correct answers are:

C) No: we would need to know if the vertex is a minimum or a maximum; and

C)( 0.25, 5.875).

Explanation:

The domain of any quadratic function is all real numbers.

The range, however, would depend on whether the quadratic was open upward or downward. If the vertex is a maximum, then the quadratic opens down and the range is all values of y less than or equal to the y-coordinate of the vertex.

If the vertex is a minimum, then the quadratic opens up and the range is all values of y greater than or equal to the y-coordinate of the vertex.

There is no way to identify from the coordinates of the vertex whether it is a maximum or a minimum, so we cannot tell what the range is.

The graph of the quadratic function is shown in the attachment. Tracing it, the vertex is at approximately (0.25, 0.5875).