N is prime given that it has 2 digits

The vertex form of the equation of a vertical parabola is given by y= 1/4p(x-h)^2 , where (h, k) is the vertex of the parabola a

matrenka [14]

Answer:

A. y = -2

B. A(6, -2)

C. use the midpoint tool to locate the vertex B(6, 1) halfway between F and A

D. up

E. divide 6 by 2; positive

F. 3

G. y = (1/12)(x -6)² +1

H. see attached

Step-by-step explanation:

A. The horizontal line 6 units below a point with y-coordinate 4 will be at ...

y = 4 -6

y = -2

__

B. The point of intersection will have the same x-coordinate as the focus (6) and the same y-coordinate as the line (-2). That point is A(6, -2).

__

C. As with every other point on the parabola, the vertex is the same distance from the focus as it is from the directrix. It will be the midpoint of segment FA. The vertex is B(6, 1).

__

D. The focus is "inside" the parabola. The focus is above the directrix, so the parabola opens upward, away from the directrix.

__

E, F. We're told to locate the directrix 6 units below the focus. The value of p is half that distance, 3 units. It can also be found by using GeoGebra to measure the length of segment FB.

__

G. Using the vertex form equation with p=3, (h, k) = (6, 1), the equation of the parabola is ...

$y=\dfrac{1}{4p}(x-h)^2+k=\dfrac{1}{4\cdot 3}(x -6)^2+1\\\\\boxed{y=\dfrac{1}{12}(x-6)^2+1}$