AnswersFL-1200330-Algebra 2 AThe Quadratic Formula

The Quadratic Formula Answers

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1
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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
2
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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
3

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

Question illustration
A
There are two complex roots.
B
There are two real roots.
C
There is one real root.
D
There is one complex root.
4

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
5

What is the discriminant of ?

Question illustration
A
76
B
94
C
106
D
124
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
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
7

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

A
–356
B
–172
C
28
D
72
8

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.
9

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.
10

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
11

Which equation can be solved using the expression for x?

Question illustration
A
10x2 = 3x + 2
B
2 = 3x + 10x2
C
3x = 10x2 – 2
D
10x2 + 2 = –3x
12

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
13

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
14

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
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

When deriving the quadratic formula by completing the square, what expression can be added to both sides of the equation to create a perfect square trinomial?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
17

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.
18

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
19

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.

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