Let 
. The tangent plane to the surface at (0, 0, 8) is
The gradient is
so the tangent plane's equation is
The normal vector to the plane at (0, 0, 8) is the same as the gradient of the surface at this point, (1, 1, 1). We can get all points along the line containing this vector by scaling the vector by 
, then ensure it passes through (0, 0, 8) by translating the line so that it does. Then the line has parametric equation
or 
, 
, and 
.
(See the attached plot; the given surface is orange, (0, 0, 8) is the black point, the tangent plane is blue, and the red line is the normal at this point)
I believe it’s graph c :)
Answer:
Folow the steps to learn what transformations were determined.
Step-by-step explanation:
First we would have to graph the parent function which is f(x) = x^2. Start by finding your x and y values. Find the y values by plugging in the x values into the parent function.
X Y
2 4
1 1
0 0
-1 1
-2 4
Once these points are plotted you can start determining what are the transformations. Find the difference between the parent function and f(x) = (x + 4)^2 + 2 by looking below.
Vertical Shifts:
f(x) + c moves up,
f(x) - c moves down.
Horizontal Shifts:
f(x + c) moves left,
f(x - c) moves right.
The parent function has to be transformed left 4 and up 2. In order to do this shift each point from earlier left 4 and then up 2. In conclusion you will have two functions graphed (parent function and the transformed function).
0-7+3=-4 because a negative and a positive make the negative go down
