Will mark the vertex form of the equation of a horizontal parabola is given by x = 1/4p (y - k)^2 + h, 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. you will use geogebra to create a horizontal parabola and write the vertex form of its equation. part a mark the focus of the parabola you are going to create at f(-5, 2). draw a vertical line that is 8 units to the right of the focus. this line will be the directrix of your parabola. what is the equation of the line? part b construct the line that is perpendicular to the directrix and passes through the focus. this line will be the axis of symmetry of the parabola. what are the coordinates of the point of intersection, a, of the axis of symmetry and the directrix of the parabola? part c explain how you can locate the vertex, v, of the parabola with the given focus and directrix. write the coordinates of the vertex. part d which way will the parabola open? explain. part e how can you find the value of p? is the value of p for your parabola positive or negative? explain. part f what is the value of p for your parabola?

Part A

The vertex form of the equation of a horizontal parabola is given by

.

where is the vertex.

Use the point tool to plot the focus, .

Move 8 units to write and draw a vertical line using the line tool.

The equation of this vertical line is .

This is the drectrix of the parabola.

See first graph in the attachment.

Part B

Construct the line that is perpendicular to the directrix using the perpendicular line tool.

Pick the perpendicular line tool from the tool bar and then select the focus and the directrix, the line .

This horizontal line is the axis of symmetry of the parabola.

The coordinates of the point of intersection,A of the axis of symmetry and the directrix of the parabola is .

See second graph in the attachment.

Part C

To locate the vertex, V of the parabola, we find the midpoint of the given focus, and the point

The vertex will then have coordinates .

Part D

The parabola will open to the left. The reason is that the parabola must open in the opposite direction to the directrix.

Part E

The absolute value of p, is the distance from either the focus or the directrix to the vertex.

The value of p will be negative because the parabola opens to the left

Part F

Since the parabola opens the left, we must have

See third graph in the attachment.

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional