AnswersPrecalculusConic Inequalities

Conic Inequalities Answers

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Which inequality is represented by the graph?

A
y ≥ –3(x + 1)2 + 5
B
y ≤ –3(x + 1)2 + 5
C
x ≥ –3(y + 1)2 + 5
D
x ≤ –3(y + 1)2 + 5
171030
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Complete the square to justify that Julia’s graph is correct.

Answers:
()2 + ()2 ≤:x + 1
()2 + ()2 ≤:y – 0
()2 + ()2 ≤:9
171031

✔ y – 0y – 1y – 2

A
✔ y – 0
B
y – 1
C
y – 2
171032

8✔ 948

A
8
B
✔ 9
C
48
171033

Some steps are shown in converting the following conic inequality from general form to standard form. Complete the conversion and identify the shape, key feature, and which ordered pair is part of the solution set.

Answers:
The conic represented in this inequality is a(n) .:ellipse with a dashed line boundary
The center is at .:(1, –2)
The ordered pair, , is a solution to the inequality.:(–2, 0)
171034

✔ (1, –2)(–2, 1)(–1, 2)(2, –1)

A
✔ (1, –2)
B
(–2, 1)
C
(–1, 2)
D
(2, –1)
171035

(1, 0)✔ (–2, 0)(1, –4)(0, –3)

A
(1, 0)
B
✔ (–2, 0)
C
(1, –4)
D
(0, –3)
171036

Which graph represents the solution set to ?

Question illustration
A
[Image: On a coordinate plane, an ellipse has center (6, n...]
Option A
B
[Image: On a coordinate plane, an ellipse has center (6, n...]
Option B
C
[Image: On a coordinate plane, an ellipse has center (nega...]
Option C
D
[Image: On a coordinate plane, an ellipse has center (nega...]
Option D
171037

Showing that (9, 1) is a solution of which inequality would justify shading inside the graph of the curve.

A
x2 – y2 > 84
B
x ≥ 3(y + 2)2 – 2
C
4(x – 4)2 – 16(y + 1)2 > 36
D
64(x – 8)2 + 12y2 < 144
171039

Miranda graphed (y + 1)2 > 6(x – 2). Which could Miranda use to justify that her graph is correct? Check all that apply.Because only the y quantity is squared, the curve is a parabola.The parabola opens right because 6 is in front of the x-quantity.There is a strict inequality so the boundary is included in the solution set.The shading is outside the parabola because (0, 0) satisfies the inequality.The values subtracted from x and y in the equation are the coordinates of the vertex which is (2, –1).

A
Because only the y quantity is squared, the curve is a parabola.
B
The parabola opens right because 6 is in front of the x-quantity.
C
There is a strict inequality so the boundary is included in the solution set.
D
The shading is outside the parabola because (0, 0) satisfies the inequality.
E
The values subtracted from x and y in the equation are the coordinates of the vertex which is (2, –1).
171040

Some steps are shown in converting the following conic inequality from general form to standard form. Complete the conversion and identify the shape, key feature, and which ordered pair is part of the solution set.

Answers:
The conic represented in this inequality is a(n) .:ellipse with a dashed line boundary
The center is at .:(1, –2)
The ordered pair, , is a solution to the inequality.:(–2, 0)

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