Answers Algebra IIQuadratics, Complex Numbers, and Systems

Quadratics, Complex Numbers, and Systems — Test Answers

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What is the distance from the origin to point cap p graphed on the complex plane?

square root of 7

square root of 29

Becca graphs the equations y is equal to negative 3 times open paren x minus 1 close paren and y is equal to x minus 5 to solve the equation negative 3 times open paren x minus 1 close paren is equal to x minus 5 Her graph is shown. What are the solution(s) of negative 3 times open paren x minus 1 close paren is equal to x minus 5 ?

negative 3

1 and 5

negative 5 and 3

What is the equation of the axis of symmetry of the graph of y plus 3 x minus 6 is equal to negative 3 times open paren x minus 2 close paren squared plus 4 ?

x is equal to negative 2

x is equal to negative 1 sixth

x is equal to 2

x is equal to 3 halves

Which equation is the inverse of y is equal to 9 x squared minus 4 ?

y is equal to the fraction with numerator plus or minus square root of x plus 4 end root and denominator 9

y is equal to plus or minus square root of x over 9 plus 4 end root

y is equal to the fraction with numerator plus or minus square root of x plus 4 end root and denominator 3

y is equal to the fraction with numerator plus or minus square root of x and denominator 3 plus 2 thirds

Which function is a quadratic function?

d times x is equal to 6 x to the 4th power plus 2 x minus 3

c times x is equal to negative 8 x squared plus 3 x minus 5

b times x is equal to 5 x cubed plus 8 x squared plus 3

A times x is equal to negative 2 x cubed plus 2 x minus 6

Use the zero product property to find the solutions to the equation 6 x squared minus 5 x is equal to 56

x is equal to negative 1 half or x is equal to 56 thirds

x is equal to negative 8 thirds or x is equal to 7 halves

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

x is equal to negative 8 or x is equal to 7 sixths

What is one of the solutions to the following system? y minus 3 is equal to x x squared minus 6 x plus 13 is equal to y

open paren 2 comma 5 close paren

open paren 8 comma 5 close paren

open paren negative 2 comma 1 close paren

open paren negative 5 comma 2 close paren

Use the zero product property to find the solutions to the equation x squared plus x minus 30 is equal to 12

x is equal to 6 or x is equal to 7

x is equal to negative 7 or x is equal to negative 6

x is equal to negative 7 or x is equal to 6

x is equal to negative 6 or x is equal to 7

If x squared plus m x plus m is a perfect-square trinomial, which equation must be true?

x squared plus m x plus m is equal to open paren x plus 1 close paren squared

x squared plus m x plus m is equal to open paren x plus 2 close paren squared

x squared plus m x plus m is equal to open paren x minus 1 close paren squared

x squared plus m x plus m is equal to open paren x plus 4 close paren squared

A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box? cap v is equal to l w h cap p is equal to 2 times open paren l plus w close paren

y is equal to 5 open paren 28 minus 2 x close paren x

y is equal to 5 open paren 14 minus x close paren x

y is equal to 5 open paren 14 minus 2 x close paren x

y is equal to 5 open paren 28 minus x close paren x

The center of a circle is at the origin on a coordinate grid. A line with a positive slope intersects the circle at open paren 0 comma 7 close paren Which statement must be true?

The slope of the line is not equal to 7 .

The slope of the line is equal to 7 .

The circle has a radius greater than 7 .

The circle has a radius equal to 7 .

Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression. He sets the expressions equal to y and graphs the equations. What is the greatest possible number of intersections for these graphs?

none

infinitely many

one

two

Which equation is the inverse of open paren x minus 4 close paren squared minus 2 thirds is equal to 6 y minus 12 ?

y is equal to 1 sixth x squared minus 4 thirds x plus 43 ninths

y is equal to negative 4 plus or minus square root of 6 x minus 34 thirds end root

y is equal to 4 plus or minus square root of 6 x minus 34 thirds end root

negative open paren x minus 4 close paren squared minus 2 thirds is equal to negative 6 y plus 12

What is the value of the expression i to the 0 power times i to the 1th power times i squared times i cubed times i to the 4th power ?

negative 1

negative i

Which graph can be used to find the solution(s) to 4 x is equal to negative 4 x ?

Image with description On a coordinate plane, the x and y axes ranges from negative 6 to 6 with an increment of 1 unit. One of the lines passes through point 4 comma 0 and 0 comma negative 4. The other line passes through point 0 comma 4 and negative 4 comma 0.

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 6 to 6 with an interval of 1 unit. One of the lines passes through (1 comma 4) and (negative 1 comma negative 4). The other line goes through (1 comma negative 4) and (negative 1 comma 4).

Image with description On a coordinate plane, the x and y axes ranges from negative 6 to 6 with an increment of 1 unit. There are two lines and both the lines are parallel to x-axis. One passes through point 0 comma negative 4 and the other line goes through point 0 comma 4.

Image with description On a coordinate plane, the x and y axes ranges from negative 6 to 6 with an increment of 1 unit. One of the lines passes through 4 comma 0 and 2 comma 2. The other line passes through negative 4 comma 0 and negative 2 comma 2.

Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression open paren negative 1 plus i close paren plus open paren 21 plus 5 i close paren ?

negative 1 plus open paren i plus 21 close paren plus 5 i

open paren negative 1 plus 21 close paren plus open paren i plus 5 i close paren

open paren negative 1 plus i close paren plus open paren 21 plus 5 i close paren plus 0

negative open paren 1 minus i close paren plus open paren 21 plus 5 i close paren

Using the quadratic formula to solve 4 x squared minus 3 x plus 9 is equal to 2 x plus 1 , what are the values of x ?

the fraction with numerator 5 plus or minus square root of 103 i and denominator 8

the fraction with numerator 5 plus or minus square root of 153 i and denominator 8

the fraction with numerator 1 plus or minus square root of 159 i and denominator 8

the fraction with numerator 1 plus or minus square root of 153 and denominator 8

Which equation demonstrates the multiplicative identity property?

open paren negative 3 plus 5 i close paren times 1 is equal to negative 3 plus 5 i

open paren negative 3 plus 5 i close paren plus 0 is equal to negative 3 plus 5 i

open paren negative 3 plus 5 i close paren times open paren negative 3 plus 5 i close paren is equal to negative 16 minus 30 i

open paren negative 3 plus 5 i close paren times open paren 3 minus 5 i close paren is equal to 16 plus 30 i

What is the solution set of the quadratic inequality x squared minus 5 is less than or equal to 0 ?

start set x such that negative 5 is less than or equal to x comma x is less than or equal to 5 end set

start set x such that negative square root of 5 is less than or equal to x comma x is less than or equal to 5 end set

start set x such that negative 5 is less than or equal to x comma x is less than or equal to square root of 5 end set

start set x such that negative square root of 5 is less than or equal to x comma x is less than or equal to square root of 5 end set

Which statement about the following equation is true? 2 x squared minus 9 x plus 2 is equal to negative 1

The discriminant is less than 0 , so there are two real roots.

The discriminant is greater than 0 , so there are two real roots.

The discriminant is less than 0 , so there are two complex roots.

The discriminant is greater than 0 , so there are two complex roots.

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Quadratics, Complex Numbers, and Systems — Test Answers

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