AnswersMO-Algebra II A-CRPerforming Operations with Complex Numbers

The Quadratic Formula Answers

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If x = –3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

A
The discriminant is negative.
B
The discriminant is –3.
C
The discriminant is 0.
D
The discriminant is positive.
2
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What is the discriminant of ?

Question illustration
A
76
B
94
C
106
D
124
3

Using the quadratic formula to solve x2 + 20 = 2x, what are the values of x?

A
1 plus-or-minus StartRoot 21 EndRoot i
Option A
B
Negative 1 plus-or-minus StartRoot 19 EndRoot i
Option B
C
1 plus-or-minus 2 StartRoot 19 EndRoot i
Option C
D
1 plus-or-minus StartRoot 19 EndRoot i
Option D
4

If is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

Question illustration
A
The discriminant is 0.
B
The discriminant is 6.
C
The discriminant is positive.
D
The discriminant is negative.
5

Using the quadratic formula to solve 5x = 6x2 – 3, what are the values of x?

A
StartFraction 5 plus-or-minus 3 StartRoot 11 EndRoot Over 12 EndFraction
Option A
B
StartFraction 5 plus-or-minus StartRoot 97 EndRoot Over 12 EndFraction
Option B
C
StartFraction 5 plus-or-minus StartRoot 47 EndRoot Over 12 EndFraction
Option C
D
StartFraction negative 5 plus-or-minus StartRoot 97 EndRoot Over 12 EndFraction
Option D
6

The first two steps in the derivation of the quadratic formula by completing the square are shown below. Which answer choice shows the correct next step?Step 1: Step 2:

Question illustration
A
mc031-3.jpg
Option A
B
mc031-4.jpg
Option B
C
mc031-5.jpg
Option C
D
mc031-6.jpg
Option D
7

Which equation shows the quadratic formula used correctly to solve 7x2 = 9 + x for x?

A
x = StartFraction negative 1 plus-or-minus StartRoot (negative 1) squared minus 4 (7) (9) EndRoot Over 2 (7) EndFraction
Option A
B
x = StartFraction 1 plus-or-minus StartRoot (negative 1) squared minus 4 (7) (9) EndRoot Over 2 (7) EndFraction
Option B
C
x = StartFraction negative 1 plus-or-minus StartRoot (negative 1) squared +4 (7) (9) EndRoot Over 2 (7) EndFraction
Option C
D
x = StartFraction 1 plus-or-minus StartRoot (negative 1) squared +4 (7) (9) EndRoot Over 2 (7) EndFraction
Option D
8

Which equation shows the quadratic formula used correctly to solve 5x2 + 3x – 4 = 0 for x?

A
x = StartFraction negative 3 plus-or-minus StartRoot (3) squared minus 4 (5) (negative 4) EndRoot Over 2 (5) EndFraction
Option A
B
x = StartFraction 3 plus-or-minus StartRoot (3) squared + 4 (5) (negative 4) EndRoot Over 2 (5) EndFraction
Option B
C
x = StartFraction 3 plus-or-minus StartRoot (3) squared minus 4 (5) (negative 4) EndRoot Over 2 (5) EndFraction
Option C
D
x = StartFraction negative 3 plus-or-minus StartRoot (3) squared + 4 (5) (negative 4) EndRoot Over 2 (5) EndFraction
Option D
9

The graph of an equation with a negative discriminant always has which characteristic?

A
no x-intercept
B
no y-intercept
C
no maximum
D
no minimum
10

Using the quadratic formula to solve 7x2 – x = 7, what are the values of x?

A
StartFraction 1 plus-or-minus StartRoot 195 EndRoot i Over 14 EndFraction
Option A
B
StartFraction 1 plus-or-minus StartRoot 197 EndRoot Over 14 EndFraction
Option B
C
StartFraction 1 plus-or-minus StartRoot 195 EndRoot Over 14 EndFraction
Option C
D
StartFraction 1 plus-or-minus StartRoot 197 EndRoot i Over 14 EndFraction
Option D
11

What is the discriminant of 9x2 + 2 = 10x?

A
–356
B
–172
C
28
D
72
12

Which equation could generate the curve in the graph below?

Question illustration
A
y = 3x2 – 2x + 1
B
y = 3x2 – 6x + 3
C
y = 3x2 – 7x + 1
D
y = 3x2 – 4x – 2
13

In the derivation of the quadratic formula by completing the square, the equation is created by forming a perfect square trinomial. What is the result of applying the square root property of equality to this equation?

Question illustration
A
mc032-2.jpg
Option A
B
mc032-3.jpg
Option B
C
mc032-4.jpg
Option C
D
mc032-5.jpg
Option D
14

Which equation has the solutions ?

Question illustration
A
2x2 + 6x + 9 = 0
B
x2 + 3x + 12 = 0
C
x2 + 3x + 3 = 0
D
2x2 + 6x + 3 = 0
15

Using the quadratic formula to solve x2 = 5 – x, what are the values of x?

A
StartFraction negative 1 plus-or-minus StartRoot 21 EndRoot Over 2 EndFraction
Option A
B
StartFraction negative 1 plus-or-minus StartRoot 19 EndRoot i Over 2 EndFraction
Option B
C
StartFraction 5 plus-or-minus StartRoot 21 EndRoot Over 2 EndFraction
Option C
D
StartFraction 1 plus-or-minus StartRoot 19 EndRoot i Over 2 EndFraction
Option D
16

Which equation has the solutions ?

Question illustration
A
3x2 – 5x + 7 = 0
B
3x2 – 5x – 1 = 0
C
3x2 – 10x + 6 = 0
D
3x2 – 10x – 1 = 0
17

Which equation could generate the curve in the graph below?

Question illustration
A
y = –2x2 + 3x – 5
B
y = –2x2 – 4x – 2
C
y = –2x2 – 16x – 28
D
y = –2x2 + 6x – 28

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