Answers Algebra IIQuadratics and Complex Numbers

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Which quadratic inequality in standard form represents the relationship in the graph?

y is less than or equal to negative 3 x squared plus 36 x minus 96

y is less than or equal to 3 x squared minus 36 x plus 96

y is less than negative 3 x squared plus 36 x minus 96

y is less than 3 x squared minus 36 x plus 96

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What is the solution set of the quadratic inequality f of x is less than or equal to 0 ?

start set x such that x is equal to negative 5 end set

varnothing

start set x such that x is equal to 5 end set

start set x such that x is in the real numbers end set

Which quadratic inequality in vertex form represents the relationship in the graph?

y is greater than open paren x minus 4 close paren squared plus 28

y is greater than or equal to 2 ninths times open paren x minus 4 close paren squared plus 28

y is greater than or equal to negative 2 times open paren x plus 4 close paren squared plus 28

y is greater than open paren x plus 4 close paren squared plus 28

Which equation is the inverse of y is equal to x squared minus 36 ?

y is equal to plus or minus square root of x plus 36

y is equal to plus or minus square root of x plus 6

y is equal to plus or minus square root of x plus 36 end root

y is equal to plus or minus square root of x squared plus 36 end root

What is the greatest possible integer value of x for which square root of x minus 5 end root is an imaginary number?

Susan plans to use 120 feet of fencing to enclose a rectangular area for a garden. Which equation best models the area, y , of the rectangular garden that she creates if one side is x feet long? cap A is equal to l w

y is equal to open paren 120 minus x close paren times x

y is equal to open paren 60 minus x close paren times open paren 60 plus x close paren

y is equal to open paren 120 minus x close paren times open paren 120 plus x close paren

y is equal to open paren 60 minus x close paren times x

Which equation is y is equal to 3 times open paren x minus 2 close paren squared minus open paren x minus 5 close paren squared rewritten in vertex form?

y is equal to 2 times open paren x minus 1 close paren squared minus 11

y is equal to 2 times open paren x minus 1 half close paren squared minus 27 halves

y is equal to 2 times open paren x minus 1 half close paren squared minus 53 fourths

y is equal to 3 times open paren x minus 7 halves close paren squared minus 27 fourths

Use the zero product property to find the solutions to the equation x squared minus 9 is equal to 16

x is equal to negative 3 or x is equal to 3

x is equal to negative 6 or x is equal to negative 3

x is equal to 7 or x is equal to 1

x is equal to negative 5 or x is equal to 5

Which function is a quadratic function?

f of x is equal to 2 x squared

b times x is equal to negative 9 x to the 4th power

k times x is equal to negative x

g of x is equal to 5 x cubed

What is the value of i raised to the 20 plus 1 power ?

negative i

negative 1

If the discriminant of a quadratic equation is 4, which statement describes the roots?

There is one real root.

There are two complex roots.

There are two real roots.

There is one complex root.

Use the zero product property to find the solutions to the equation x squared minus x minus 6 is equal to 0

x is equal to negative 2 or x is equal to 3

x is equal to negative 3 or x is equal to negative 2

x is equal to 2 or x is equal to 3

x is equal to negative 3 or x is equal to 2

Which graph represents the solution set for the quadratic inequality x squared plus 2 x plus 1 is greater than 0 ?

Image with description A number line, labeled x, is marked with integers from negative 5 to 5. An open circle is at negative 1, and a thick line extends indefinitely in both directions with arrows at each end.

Image with description A number line, labeled x, is marked with integers from negative 5 to 5. An open circle is at 1, and a thick line extends from this point to the right, with an arrow indicating it continues indefinitely.

Image with description A number line, labeled x, is marked with integers from negative 5 to 5. A closed circle is at negative 1, and a thick line extends from this point to the right, with an arrow indicating it continues indefinitely.

Image with description A number line, labeled x, is marked with integers from negative 5 to 5. A closed circle is at negative 1, and a thick line extends from this point to the left, with an arrow indicating it continues indefinitely.

Which equation is the inverse of y is equal to 7 x squared minus 10 ?

y is equal to plus or minus square root of the fraction with numerator x plus 10 and denominator 7 end root

y is equal to the fraction with numerator plus or minus square root of x and denominator 7 plus or minus the fraction with numerator square root of 10 and denominator 7

y is equal to plus or minus square root of x over 7 plus 10 end root

y is equal to the fraction with numerator plus or minus square root of x plus 10 end root and denominator 7

Using the quadratic formula to solve 11 x squared minus 4 x is equal to 1 , what are the values of x ?

2 over 11 plus or minus the fraction with numerator square root of 15 and denominator 11

2 over 11 plus or minus the fraction with numerator square root of 7 and denominator 11

2 over 11 plus or minus the fraction with numerator square root of 7 i and denominator 11

2 over 11 plus or minus the fraction with numerator 2 square root of 15 and denominator 11

Louis used a quadratic equation to model the height, y , of a falling object x seconds after it is dropped. Which ordered pair generated by this model should be discarded because the values are unreasonable?

open paren 5 comma 3 halves close paren

open paren 9 fourths comma 24 close paren

open paren negative 4 comma 1 close paren

open paren 6 comma 0 close paren

Which expression is equivalent to open paren 4 plus 6 i close paren squared ?

8 plus 12 i

negative 20 plus 48 i

16 minus 36 i

20 plus 48 i

Which equation is an example of the commutative property of multiplication?

open paren 4 plus 2 i close paren is equal to open paren 4 plus 2 i plus 0 close paren

open paren 4 plus 2 i close paren times open paren 3 minus 5 i close paren is equal to open paren 3 minus 5 i close paren times open paren 4 plus 2 i close paren

open paren 4 plus 2 i close paren times open paren 3 minus 5 i close paren is equal to open paren 4 plus 2 i close paren times open paren 3 minus 5 i close paren times 1

open paren 4 plus 2 i close paren is equal to open paren 2 i plus 4 close paren

What are the values of x in the equation x squared minus 6 x plus 9 is equal to 25 ?

x is equal to 1 or x is equal to 11

x is equal to 2 or x is equal to negative 8

x is equal to negative 1 or x is equal to negative 11

x is equal to negative 2 or x is equal to 8

What is the vertex of the graph of y plus 2 x plus 3 is equal to negative open paren x plus 2 close paren squared plus 1 ?

open paren negative 3 comma negative 33 close paren

open paren negative 3 comma 3 close paren

open paren 3 comma negative 24 close paren

open paren 3 comma 21 close paren

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