AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Writing Two-Variable Quadratic Inequalities

Writing Two-Variable Quadratic Inequalities — Unit test Answers

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1
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For what values of m does the graph of y = mx2 – 5x – 2 have no x-intercepts?

A
m greater-than negative StartFraction 25 Over 8 EndFraction
Option A
B
m less-than negative StartFraction 25 Over 8 EndFraction
Option B
C
m less-than StartFraction 25 Over 8 EndFraction
Option C
D
m greater-than StartFraction 25 Over 8 EndFraction
Option D
2
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What is the greatest possible integer value of x for which is an imaginary number?

Question illustration
A
3
B
4
C
5
D
6
3

Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form?

A
y = 3 (x minus seven-halves) squared minus StartFraction 27 Over 4 EndFraction
Option A
B
y = 2 (x minus 1) squared minus 11
Option B
C
y = 2 (x minus one-half) squared minus StartFraction 53 Over 4 EndFraction
Option C
D
y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction
Option D
4

Which equation represents a graph with a vertex at (1, –6)?

A
y = 3x2 + 6x – 3
B
y = 3x2 – 6x – 3
C
y = 3x2 – 8x – 1
D
y = 3x2 – 3x – 6
5

Which values of x and y would make the following expression represent a real number? (6 + 3i)(x + yi)

A
x = 6, y = 0
B
x = –3, y = 0
C
x = 6, y = –3
D
x = 0, y = –3
6

Which equation is y = –6x2 + 3x + 2 rewritten in vertex form?

A
y = negative 6 (x minus 1) squared + 8
Option A
B
y = negative 6 (x + one-fourth) squared + thirteen-eighths
Option B
C
y = negative 6 (x minus one-fourth) squared + nineteen-eighths
Option C
D
y = negative 6 (x minus one-half) squared + seven-halves
Option D
7

When graphed, which parabola opens downward?

A
y = –3x2
B
y = (x – 3)2
C
y = one-third x squared
Option C
D
y = x2 – 3
8

Which property of multiplication is shown below? If x = 3 + 4i and y = 5 + 6i, x × y = y × x.

A
commutative property
B
identity property
C
distributive property
D
associative property
9

Which point shows the location of 5 – 2i on the complex plane below?

Question illustration
A
point A
B
point B
C
point C
D
point D
10

The graph of a quadratic inequality is shown.

Question illustration
A
y greater-than-or-equal-to two-ninths (x minus 4) squared + 28
Option A
B
y greater-than (x minus 4) squared + 28
Option B
C
y greater-than-or-equal-to negative 2 (x + 4) squared + 28
Option C
D
y greater-than (x + 4) squared + 28
Option D
11

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

A
There are two complex roots.
B
There are two real roots.
C
There is one real root.
D
There is one complex root.
12

The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 22i. Which statement must be true about the complex numbers?

A
The complex numbers have equal imaginary coefficients.
B
The complex numbers have equal real numbers.
C
The complex numbers have opposite imaginary coefficients.
D
The complex numbers have opposite real numbers.
13

What is the value of i 97 – i?

A
–i
B
0
C
–2i
D
i Superscript 96
Option D
14

Which inequality in vertex form represents the region less than the quadratic function with vertex (8, 24) and the point (3, 99) on the boundary?

A
Option
Option A
B
y < 3(x + 8)2 + 24
C
Option
Option C
D
y < 3(x – 8)2 + 24
15

For which value of m does the graph of y = 18x2 + mx + 2 have exactly one x-intercept?

A
0
B
9
C
12
D
16

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