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.

easy its decreasing

step-by-step explanation:

because its top point is at the to of the graph on the left side (atleast from the veiw i see it) now if that top point wast in the lower part of the graph it would be increasing hope this have a nice day

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true