Question

Will someone explain this to me?
a. The vertex form of the equation of a vertical parabola is given by , where (h, k) is the vertex of the parabola and the absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to the directrix.

Answer 1

You will use the GeoGebra geometry tool to create a vertical parabola and write the vertex form of its equation.
i:i. Mark the focus of the parabola you are going to create at F(6, 4). Draw a horizontal line that is 6 units below the focus. This line will be the directrix of your parabola. What is the equation of the line?

i am super confused on what to do

Answer 2

hey do u still need help?

Answer 3

"focus of the parabola at (6, 4). horizontal line that is 6 units below the focus will be the directrix"
directrix: y = -2

Determine the orientation of the parabola:
The directrix is horizontal, so the parabola is vertical.
The focus lies above the directrix, so the parabola opens upwards.
Equation of up-opening parabola:
 y = a(x - h)² + k

The vertex is halfway between focus and directrix.
vertex (6, 1)
h = 6
k = 1

p = distance between focus and vertex = 3
a = 1/(4p) = 1/12

The equation of the parabola:
y = (1/12)(x - 6)² + 1

Answer 4

thank you