AnswersFL-1200710-Mathematics for College Algebra ACompleting the Square (Continued)

The Quadratic Formula Answers

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1
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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
2
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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.
3

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
4

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
5

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.
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

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
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

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
10

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

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