Find the vertex, focus, directrix, and focal width of the parabola. (5 points) negative 1 divided by 16 times x squared = y

Step-by-step explanation:

Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16 ⇒ answer (a)

Step-by-step explanation:

* Lets revise some facts about the parabola

- Standard form equation for a parabola of vertex at (0 , 0)

- If the equation is in the form  x² =  4py, then  

- The axis of symmetry is the y-axis,  x = 0  

- 4p  equal to the coefficient of y in the given equation to

 solve for  p

- If  p  >  0, the parabola opens up.

- If  p <  0, the parabola opens down.

- Use  p  to find the coordinates of the focus,  (0  ,  p)

- Use  p  to find equation of the directri ,   y= − p

- Use  p  to find the endpoints of the focal diameter,  (±2p  ,  p)

* Now lets solve the problem

- The vertex of the parabola is (0 , 0)

∵ -1/16x² = y ⇒ multiply each side by -16

∴ x² = -16y

∴ 4p = -16 ⇒ ÷ 4 tbe both sides

∴ p = -4

∵ The focus is (0 , p)

∴ The focus is (0 , -4)

∵ The directrix is y = -p

∴ The directrix is y = -(-4) = 4 ⇒ y = 4

∵ The endpoints of the focal diameter,  (±2p  ,  p)

∴ The focal width = 2p - (-2p) = 4p

∴ The focal width = 4 ×  I-4I = 16

* Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

6 cm

step-by-step explanation: