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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)

B)(-0.25, 5.875)

C)( 0.25, 5.875)

D)( 0.25, 6)

Verified Answer :

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).

View image MsEHolt

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