Aparabola has its vertex at (2, 2), and the equation of its directrix is y = 2.5. the equation that represents the parabola is

In vertex form the equation is

In standard form the equation is

Step-by-step explanation:

The equation of the directrix tells us that this is an x-squared parabola.  Because the directrix is above the vertex, the parabola will open downward.  The vertex form of this equation is:

where p is the number of units between the directrix and the vertex.  The number of units here is .5 or 1/2.  Filling in the coordinates of the vertex and the p value of 1/2:

Simplifying we have:

Divide both sides by 2 to get:

Add 2 to both sides to get the final vertex form:

If you want that in standard form, you first need to expand the squared term to get:

Order of operations tells us that we have to distribute in the -1/2 first to get:

which simplifies to the standard form:

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).