AnswersFL-1200330-Algebra 2 AWriting Two-Variable Quadratic Inequalities

Lesson 3.7: Writing Two-Variable Quadratic Inequalities Answers

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On a coordinate plane, a parabola with a dashed boundary line opens down. It goes through (negative 8, 0), has a vertex at (negative 6, 2), and goes through (negative 4, 0).

Question illustration
A
y less-than negative x squared minus 12 x minus 32
Option A
B
y less-than negative one-half x squared minus 6 x minus 16
Option B
C
y less-than negative one-half x squared + 6 x minus 16
Option C
D
y less-than negative x squared + 12 x minus 32
Option D
2
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Which inequality in vertex form represents the region less than or equal to the quadratic function with vertex (–6, 12) and includes the point (–9, 15) on the boundary?

A
y less-than-or-equal-to one-third (x minus 6) squared + 12
Option A
B
y less-than-or-equal-to one-third (x + 6) squared + 12
Option B
C
y less-than-or-equal-to 3 (x + 6) squared + 12
Option C
D
y less-than-or-equal-to 3 (x minus 6) squared + 12
Option D
3

Which statement describes the quadratic inequality in factored form that represents the relationship greater than or equal to the quadratic equation containing the point (6, –8) on the boundary and zeros –4 and 10?

A
y ≥ –0.2(x + 4)(x – 10)
B
y ≥ 0.2(x + 4)(x – 10)
C
y ≥ 0.2(x – 4)(x + 10)
D
y ≥ –0.2(x – 4)(x + 10)
4

The graph shows a company’s profit. The shaded region represents values when the profits were greater than projected.

Question illustration
A
y greater-than-or-equal-to (x minus 50) squared + 625
Option A
B
y greater-than-or-equal-to negative (x + 50) squared + 625
Option B
C
y greater-than-or-equal-to (x + 50) squared + 625
Option C
D
y greater-than-or-equal-to negative (x minus 50) squared + 625
Option D
5

Which inequality in vertex form represents the region less than the quadratic function with vertex (–2, 2) and includes the point (–4, 14) on the boundary?

A
y < 3(x + 2)2 + 2
B
y < –3(x + 2)2 + 2
C
y < 3(x – 2)2 + 2
D
y < –3(x – 2)2 + 2
6

Which inequality in factored form represents the region less than the quadratic function with zeros –40 and –50 and includes the point (–55, –75) on the boundary line?

A
y < –(x – 40)(x – 50)
B
y ≤ –(x + 40)(x + 50)
C
y ≤ –(x – 40)(x – 50)
D
y < –(x + 40)(x + 50)
7

After 4 seconds, a launched projectile reaches a maximum height of 60 feet. The projectile is launched from a height of 12 feet.

A
y ≥ –3x2 + 24x + 12
B
y ≥ 3x2 – 24x – 12
C
y ≤ –3x2 + 24x +12
D
y ≤ 3x2 – 24x – 12
8

On a coordinate plane, a parabola with a dashed boundary line opens up. It goes through (negative 6, 0), (negative 4, negative 44), has a vertex at (6, negative 160), and goes through (18, 0).

Question illustration
A
y greater-than-or-equal-to (x + 6)(x minus 18)
Option A
B
y greater-than (x minus 6)(x + 18)
Option B
C
y greater-than (x + 6)(x minus 18)
Option C
D
Option
Option D
9

The graph represents the potential area of a concrete rectangle, based on length and width.

Question illustration
A
y less-than negative 2 (x + 16) squared minus 32
Option A
B
y less-than negative one-half (x minus 16) squared + 32
Option B
C
y less-than negative 2 (x minus 16) squared + 32
Option C
D
y less-than negative one-half (x + 16) squared minus 32
Option D
10

Which is the inequality in factored form that represents the region greater than or equal to the quadratic function with zeros –3.5 and 11.5 and includes the point (8.5, –54) on the boundary?

A
y greater-than-or-equal-to three-halves (x minus 3.5)(x + 11.5)
Option A
B
y greater-than-or-equal-to negative three-halves (x + 3.5)(x minus 11.5)
Option B
C
y greater-than-or-equal-to negative three-halves (x minus 3.5)(x + 11.5)
Option C
D
y greater-than-or-equal-to three-halves (x + 3.5) (x minus 11.5)
Option D

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