AnswersAdvanced Algebra Concepts and ConnectionsWriting Two-Variable Quadratic Inequalities

Writing Two-Variable Quadratic Inequalities — Quiz Answers

10 verified answers
1
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A projectile is launched from a height of 12 feet and follows a parabolic trajectory. After 4 seconds, the projectile reaches a maximum height of 60 feet. If all the experiments that followed met or exceeded this path, which quadratic inequality in standard form contains the points in the later experiments?

A
y is less than or equal to 3 x squared minus 24 minus 12
B
y is less than or equal to negative 3 x squared plus 24 plus 12
C
y is greater than or equal to negative 3 x squared plus 24 plus 12
D
y is greater than or equal to 3 x squared minus 24 minus 12
2
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Which inequality in vertex form represents the region less than the quadratic function with vertex open paren negative 2 comma 2 close paren and includes the point open paren negative 4 comma 14 close paren on the boundary?

A
y is less than negative 3 times open paren x plus 2 close paren squared plus 2
B
y is less than 3 times open paren x minus 2 close paren squared plus 2
C
y is less than negative 3 times open paren x minus 2 close paren squared plus 2
D
y is less than 3 times open paren x plus 2 close paren squared plus 2
3

Which inequality in vertex form represents the region less than or equal to the quadratic function with vertex open paren negative 6 comma 12 close paren and includes the point open paren negative 9 comma 15 close paren on the boundary?

A
y is less than or equal to 3 times open paren x minus 6 close paren squared plus 12
B
y is less than or equal to 3 times open paren x plus 6 close paren squared plus 12
C
y is less than or equal to 1 third times open paren x plus 6 close paren squared plus 12
D
y is less than or equal to 1 third times open paren x minus 6 close paren squared plus 12
4

The parabolic path of a launched projectile contains the vertex open paren 5 comma 120 close paren and the point open paren 25 comma 80 close paren 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?

A
y is greater than or equal to negative 1 tenth times open paren x plus 5 close paren squared plus 120
B
y is less than or equal to negative 1 tenth times open paren x minus 5 close paren squared plus 120
C
y is greater than or equal to negative 1 tenth times open paren x minus 5 close paren squared plus 120
D
y is less than or equal to negative 1 tenth times open paren x plus 5 close paren squared plus 120
5

Which is the inequality in factored form that represents the region greater than or equal to the quadratic function with zeros negative 3 point 5 and 11 point 5 and includes the point open paren 8 point 5 comma negative 54 close paren on the boundary?

A
y is greater than or equal to negative 3 halves open paren x plus 3 point 5 close paren open paren x minus 11 point 5 close paren
B
y is greater than or equal to 3 halves open paren x plus 3 point 5 close paren open paren x minus 11 point 5 close paren
C
y is greater than or equal to 3 halves open paren x minus 3 point 5 close paren open paren x plus 11 point 5 close paren
D
y is greater than or equal to negative 3 halves open paren x minus 3 point 5 close paren open paren x plus 11 point 5 close paren
6

Which inequality is less than the quadratic function with zeros negative 7 and 1 and includes the point open paren 2 comma 27 halves close paren on the boundary?

A
y is less than negative 3 halves x squared minus 9 x plus 21 halves
B
y is less than 3 halves x squared plus 9 x minus 21 halves
C
y is less than negative 3 halves x squared plus 9 x plus 21 halves
D
y is less than 3 halves x squared minus 9 x minus 21 halves
7

Which inequality in standard form represents the region greater than the quadratic function with zeros negative 3 and 6 and includes the point open paren negative 2 comma negative 16 close paren on the boundary line?

A
y is greater than 2 x squared minus 6 x minus 36
B
y is greater than 2 x squared plus 6 x plus 36
C
y is greater than 1 half x squared plus 3 halves x minus 9
D
y is greater than 1 half x squared minus 3 halves x minus 9
8

Which inequality in vertex form represents the region less than or equal to the quadratic function with vertex open paren negative 6 comma 12 close paren and includes the point open paren negative 9 comma 15 close paren on the boundary?

A
y is less than or equal to 3 times open paren x minus 6 close paren squared plus 12
B
y is less than or equal to 1 third times open paren x minus 6 close paren squared plus 12
C
y is less than or equal to 1 third times open paren x plus 6 close paren squared plus 12
D
y is less than or equal to 3 times open paren x plus 6 close paren squared plus 12
9

Which inequality in factored form represents the region less than the quadratic function with zeros negative 40 and negative 50 and includes the point open paren negative 55 comma negative 75 close paren on the boundary line?

A
y is less than negative open paren x plus 40 close paren times open paren x plus 50 close paren
B
y is less than or equal to negative open paren x minus 40 close paren times open paren x minus 50 close paren
C
y is less than negative open paren x minus 40 close paren times open paren x minus 50 close paren
D
y is less than or equal to negative open paren x plus 40 close paren times open paren x plus 50 close paren
10

A projectile is launched from a height of 12 feet and follows a parabolic trajectory. After 4 seconds, the projectile reaches a maximum height of 60 feet. If all the experiments that followed met or exceeded this path, which quadratic inequality in standard form contains the points in the later experiments?

A
y is greater than or equal to negative 3 x squared plus 24 plus 12
B
y is greater than or equal to 3 x squared minus 24 minus 12
C
y is less than or equal to 3 x squared minus 24 minus 12
D
y is less than or equal to negative 3 x squared plus 24 plus 12

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