Writing Two-Variable Quadratic Inequalities

Question 1

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).

Revolt · Accepted Answer

y less-than negative one-half x squared minus 6 x minus 16

Question 2

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?

Revolt · Accepted Answer

y greater-than-or-equal-to three-halves (x + 3.5) (x minus 11.5)

Question 3

On a coordinate plane, a parabola with a solid boundary line opens up. It goes through (negative 1, 0), has a vertex at (4, negative 125), and goes through (9, 0).

Revolt · Accepted Answer

y greater-than-or-equal-to 5 x squared minus 40 x minus 45

Question 4

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

Revolt · Accepted Answer

y greater-than-or-equal-to negative (x minus 50) squared + 625

Question 5

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

Revolt · Accepted Answer

y less-than negative one-half (x minus 16) squared + 32

Question 6

On a coordinate plane, a parabola with a solid boundary line opens down. It goes through (negative 5, 0), has a vertex at (5, 300), and goes through (15, 0).

Revolt · Accepted Answer

y greater-than-or-equal-to minus 3 x squared + 30 x + 225

Question 7

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?

Revolt · Accepted Answer

y < 3(x + 2)2 + 2

Question 8

On a coordinate plane, a parabola with a solid boundary line opens down. It goes through (negative 8, 0), (0, 24), and goes through (12, 0).

Revolt · Accepted Answer

Answer image: https://media.edgenuity.com/evresources/undefined8106-01-03-11.png

Question 9

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

Revolt · Accepted Answer

y ≤ –3x2 + 24x +12

Question 10

The path of a launched projectile contains the vertex (5, 120) and the point (25, 80) on the boundary. If all the experiments that followed met or exceeded this path, which quadratic inequality in standard form contains the points in the later experiments?

Revolt · Accepted Answer

y greater-than-or-equal-to negative one-tenth (x minus 5) squared + 120

Writing Two-Variable Quadratic Inequalities Answers

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