Answers CMS 2026-2027 Foundations of Math 3 INITIAL CREDITQuadratics and Complex Numbers

Quadratics and Complex Numbers — 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

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What is the domain of the function?

all real numbers greater than but not equal to 0

all real numbers less than or equal to 0

all real numbers greater than or equal to 0

all real numbers

Which represents the reflection of f of x is equal to square root of x over the y -axis?

Image with description A coordinate plane with a curve. The x and y axes are labeled form negative 10 to 10 in increments of 2. The curve begins at the point 0 comma 0 and extends toward the upper left, passing through the point negative 4 comma 2.

Image with description A coordinate plane with a curve. The x and y axes are labeled form negative 10 to 10. The curve begins at the point 0 comma 0 and extends toward the upper left, passing through the points negative 1, comma 1, negative 4 comma, 2, and negative 9 comma, 3.

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'f of x' Row 2: Column 1, 'negative 1'; Column 2, '1' Row 3: Column 1, '0'; Column 2, '0' Row 4: Column 1, '1'; Column 2, 'negative 1' Row 5: Column 1, '4'; Column 2, 'negative 2'

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'f of x' Row 2: Column 1, 'negative 1'; Column 2, 'undefined' Row 3: Column 1, '0'; Column 2, '0' Row 4: Column 1, '1'; Column 2, '1' Row 5: Column 1, '4'; Column 2, '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 open paren 1 minus i close paren plus open paren 21 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 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

Which values of x and y would make the following expression represent a real number? open paren 4 plus 5 i close paren times open paren x plus y i close paren

x is equal to 4 , y is equal to 5

x is equal to negative 4 , y is equal to 0

x is equal to 0 , y is equal to 5

x is equal to 4 , y is equal to negative 5

Which equation demonstrates the multiplicative identity property?

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

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 1 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

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 minus 1 close paren squared

x squared plus m x plus m is equal to open paren x plus 4 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 plus 1 close paren squared

Solve for x in the equation x squared minus 8 x plus 41 is equal to 0

x is equal to negative 4 plus or minus 5 i

x is equal to negative 4 plus or minus square root of 37 i

x is equal to 4 plus or minus square root of 37 i

x is equal to 4 plus or minus 5 i

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 statement about the following equation is true? 3 x squared minus 8 x plus 5 is equal to 5 x squared

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

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

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

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

Which equation represents a graph with a vertex at open paren negative 3 comma 2 close paren ?

y is equal to 4 x squared plus 16 x plus 13

y is equal to 4 x squared minus 24 x plus 38

y is equal to 4 x squared plus 12 x plus 2

y is equal to 4 x squared plus 24 x plus 38

Which phrase best describes the translation from the graph y is equal to open paren x minus 5 close paren squared plus 7 to the graph of y is equal to open paren x plus 1 close paren squared minus 2 ?

6 units left and 9 units down

6 units right and 9 units down

6 units right and 9 units up

6 units left and 9 units up

Solve for x in the equation x squared minus 12 x plus 36 is equal to 90

x is equal to 6 plus or minus 2 square root of 7

x is equal to 12 plus or minus 3 square root of 10

x is equal to 6 plus or minus 3 square root of 10

x is equal to 12 plus or minus 3 square root of 22

What is the simplified form of square root of four hundred x to the hundredth power end root ?

two hundred x to the tenth power

twenty x to the tenth power

two hundred x to the fiftieth power

twenty x to the fiftieth power

Which equation is y is equal to 9 x squared plus 9 x minus 1 rewritten in vertex form?

y is equal to 9 times open paren x plus 1 half close paren squared plus 5 fourths

y is equal to 9 times open paren x plus 1 half close paren squared minus 1

y is equal to 9 times open paren x plus 1 half close paren squared minus 5 fourths

y is equal to 9 times open paren x plus 1 half close paren squared minus 13 fourths

In which quadrant is the number 6 minus 8 i located on the complex plane?

III

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 complex roots.

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

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

Which is the graph of g of x is equal to square root of x minus 16 end root ?

Image with description A coordinate plane displays the x-axis labeled from 4 to 44 in increments of 4 and the y-axis labeled from 1 to 10 in increments of 1. An increasing curve begins at approximately 0 comma 4, rises steeply at first, then gradually levels off, passing near 4 comma 6, 12 comma 7.5, 24 comma 9, and ending at approximately 36 comma 10.

Image with description A coordinate plane displays the x-axis labeled from 4 to 44 in increments of 4 and the y-axis labeled from 1 to 10 in increments of 1. An increasing curve begins at approximately 4 comma 4, rises steeply at first, then gradually levels off, passing near 8 comma 6, 16 comma 7.5, 28 comma 9, and ending at approximately 40 comma 10.

Image with description A coordinate plane with x-axis labeled from 4 to 44 in increments of 4 and y-axis labeled from 1 to 10 in increments of 1. A smooth curve originates from 4 comma 0, moves right and passes through the point 20 comma 4 and terminates at the point 40 comma 6.

Image with description A coordinate plane with x-axis labeled from 4 to 44 in increments of 4 and y-axis labeled from 1 to 10 in increments of 1. A smooth curve originates from 16 comma 0, moves right and passes through the points 20 comma 2 and terminates at the point 40 comma 5.

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 1 plus or minus square root of 153 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

What is the simplest form of square root of three comma zero two five ?

5 squared times 11 squared

5 squared plus 11 squared

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