Parabolas Assignment and Quiz

A parabola has a vertex at the origin. The equation of the directrix of the parabola is y = 3. What are the coordinates of its focus?

(0,-3)

A parabola is represented by the equation x2 = 4y. What are the coordinates of the focus of the parabola?

(0,1)

The shape of a satellite dish can be described as parabolic. Satellite dishes are this shape because radio waves are reflected from the surface of the dish and received into the focus. If the graph of the satellite dish is given by the equation x2 = 8y, what are the coordinates of the focus?

(0,2)

A general formula for a parabola is y2 = 4px. What is the value of p in the equation y2 = -4x?

-1

A parabola has a vertex at (0,0). The focus of the parabola is located at (4,0). What is the equation of the directrix?

-4

Which graph represents the function y2 = −16x?

A

Describe the key features of the parabola y2 = 8x.

P would be equal to 2. The focus would be (2,0) The directrix would be -2. The parabola would open to the right.

Which statements are true for the equation x2 = −4y? Check all that apply.

The axis of symmetry is x = 0. The focus is at (0, -1). The value of p = −1.

If the directrix of a parabola is the horizontal line y = 3, what is true of the parabola?

The focus is at (0, -3), and the equation for the parabola is x2 = -12y.

When the focus and directrix are used to derive the equation of a parabola, two distances were set equal to each other. The distance between the directrix and ________________ is set equal to the distance between the __________ and the same point on the parabola.

a point on the parabola focus

A parabola can be represented by the equation y2 = -x. What are the coordinates of the focus and the equation of the directrix?

focus: (-1/4,0); directrix: x = 1/4

A parabola has a vertex at (0,0). The equation for the directrix of the parabola is x = -4. In which direction does the parabola open?

right

A parabola has a vertex at (0,0). The focus of the parabola is located on the positive x-axis. Which part of the graph will the directrix pass through?

the negative part of the x-axis

A parabola is represented by the equation y2 = 5x. Which equation represents the directrix?

x = -5/4

The focus of a parabola is located at (0,-2). The directrix of the parabola is represented by y = 2. Which equation represents the parabola?

x2 = -8y

The derivation for the equation of a parabola with a vertex at the origin is started below. (x)2 + (y - p)2 = (0)2 + (y + p)2 x2 + y2 - 2py + p2 = y2 + 2py + p2 If the equation is further simplified, which equation for a parabola does it become?

x2 = 4py

Which equation represents the parabola shown on the graph?

x2 = 6y

Lauren describes a parabola where the focus has a positive, nonzero x coordinate. Which parabola(s) could Lauren be describing? Check all that apply.

y2 = x y2 = 10x y2 = 5x

The parabola has a focus at (−3, 0) and directrix y = 3. What is the correct equation for the parabola?

y2 = −12x