Answers2627 ALGEBRA II AThe Quadratic Formula

The Quadratic Formula Answers

10 verified answers8 views
1
Free Preview

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
Free Preview

What is the discriminant of ?

Question illustration
A
76
B
94
C
106
D
124
3

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
4

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
5

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
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

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
mc030-2.jpg
Option A
B
mc030-3.jpg
Option B
C
mc030-4.jpg
Option C
D
mc030-5.jpg
Option D
8

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
9

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
10

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
11

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
12

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
13

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
14

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
15

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
16

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
17

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
18

Which equation has the solutions ?

Question illustration
A
x2 + 2x + 4 = 0
B
x2 – 2x + 4 = 0
C
x2 + 2x – 4 = 0
D
x2 – 2x – 4 = 0
19

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

Did you find these answers helpful?

More from this Course

Quiz
13 verified answers

The Quadratic Formula

Quiz
16 verified answers

The Quadratic Formula

Quiz
15 verified answers

The Quadratic Formula