Describe how the graph of y = x2 can be transformed to the graph of the given equation. y = (x - 2)2 - 15 (5 points)
a. shift the graph of y = x2 left 2 units and then down 15 units.
b. shift the graph of y = x2 down 2 units and then left 15 units.
c. shift the graph of y = x2 right 2 units and then down 15 units.
d. shift the graph of y = x2 right 2 units and then up 15 units.

  c.  Shift the graph of y = x^2 right 2 units and then down 15 units

Step-by-step explanation:

Replacing x in f(x) with (x-a) shifts the graph to the right by "a" units. Adding "b" to f(x) to make it f(x)+b shifts the graph up by "b" units.

Here, we have "a" = 2 and "b" = -15 to turn f(x) = x^2 into f(x-2)-15 = (x-2)^2-15. So, the graph is shifted ...

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.