Parabolas

Question 1

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 parabola opens up.The parabola opens right.The value of p = −1.The equation for the directrix is y = 0.

Revolt · Accepted Answer

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

Question 2

directix✔ focusoriginx-axis

Revolt · Accepted Answer

focus

Question 3

When the focus and directrix are used to derive the equation of a parabola, two distances were set equal to each other.

Revolt · Accepted Answer

✔ a point on the parabola; 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; The distance between the directrix and is set equal to the distance between the and the same point on the parabola.: focus

Question 4

directix✔ focusoriginx-axis

Revolt · Accepted Answer

✔ focus

Question 5

If the equation is further simplified, which equation for a parabola does it become?

Revolt · Accepted Answer

x2 = 4py

Question 6

Lauren describes a parabola where the focus has a positive, nonzero x coordinate. Which parabola(s) could Lauren be describing? Check all that apply.x2 = 4yx2 = –6yy2 = x y2 = 10xy2 = –3xy2 = 5x

Revolt · Accepted Answer

y2 = x; y2 = 10x; y2 = 5x

Question 7

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?

Revolt · Accepted Answer

⇒ 2: 2

Question 8

Which graph represents the function y2 = −16x?

Revolt · Accepted Answer

[Image: On a coordinate plane, a parabola opens to the lef...]

Question 9

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

Revolt · Accepted Answer

y2 = −12x

Question 10

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

Revolt · Accepted Answer

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

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