AnswersAlgebra 2Writing Two-Variable Quadratic Inequalities

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Which inequality shows the region represented by the inequality in vertex form?

A
y is greater than or equal to negative open paren x plus 50 close paren squared plus 625
B
y is greater than or equal to open paren x plus 50 close paren squared plus 625
C
y is greater than or equal to negative open paren x minus 50 close paren squared plus 625
D
y is greater than or equal to open paren x minus 50 close paren squared plus 625
2
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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 minus 3 point 5 close paren open paren x plus 11 point 5 close paren
C
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
D
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
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 open paren 6 comma negative 8 close paren on the boundary and zeros negative 4 and 10 ?

A
y is greater than or equal to 0 point 2 open paren x minus 4 close paren open paren x plus 10 close paren
B
y is greater than or equal to 0 point 2 open paren x plus 4 close paren open paren x minus 10 close paren
C
y is greater than or equal to negative 0 point 2 open paren x minus 4 close paren open paren x plus 10 close paren
D
y is greater than or equal to negative 0 point 2 open paren x plus 4 close paren open paren x minus 10 close paren
4

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 or equal to 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 plus 40 close paren times open paren x plus 50 close paren
D
y is less than negative open paren x minus 40 close paren times open paren x minus 50 close paren
5

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 1 third 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 3 times open paren x minus 6 close paren squared plus 12
6

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 plus 6 x plus 36
B
y is greater than 1 half x squared plus 3 halves x minus 9
C
y is greater than 2 x squared minus 6 x minus 36
D
y is greater than 1 half x squared minus 3 halves x minus 9
7

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 greater than or equal to negative 1 tenth times open paren x minus 5 close paren squared plus 120
C
y is less 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
8

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 3 times open paren x plus 2 close paren squared plus 2
B
y is less than negative 3 times open paren x minus 2 close paren squared plus 2
C
y is less than negative 3 times open paren x plus 2 close paren squared plus 2
D
y is less than 3 times open paren x minus 2 close paren squared plus 2
10

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

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