AnswersAlgebra III AQuadratic Inequalities

Quadratic Inequalities Answers

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3

Select the inequality that represents the problem.

A
x2 – 3 x – 81 0
Option A
B
x2 – 3 x – 27 0
Option B
C
x2 – 12 x – 27 0
Option C
D
x2 – 12 x 0
Option D
5

{x | x = 6} {x | –6 x < 6}{ }{ and }

A
{x | x = 6}
Option A
B
{x | –6 x < 6}
Option B
C
{ }
Option C
D
{ and }
Option D
E
Option
Option E
6

all real numbers✔ the empty setx = 2 or x = 4x = –2 or x = 4

A
all real numbers
B
✔ the empty set
C
x = 2 or x = 4
D
x = –2 or x = 4
7

–8, –6, –4–10, –6, 0 –6, 0, 6–6, 0, 10

A
–8, –6, –4
B
–10, –6, 0
C
–6, 0, 6
D
–6, 0, 10
8

Choose the graph of y < –x2 + 4x + 5.

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

Question text not available

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

Question text not available

Answer:

To graph y ≤ -x^2 + 2x, first graph the boundary parabola y = -x^2 + 2x. The parabola opens downward because the leading coefficient is negative. Find the vertex by using x = -b/(2a) = -2/(2*-1) = 1; the vertex is at (1, 1). The x-intercepts are at x=0 and x=2. Use a solid line for the boundary because the inequality is 'less than or equal to'. Finally, test a point like (1, 0). Since 0 ≤ -1^2 + 2(1) (0 ≤ 1) is true, shade the region inside the parabola.

11

In your description, did you

A
graph the parabola opening down with the vertex at (1, 1)?
B
factor the quadratic as y –1(x)(x – 2)?
Option B
C
find the roots of the parabola to be 0 and 2?
D
graph the parabola with a solid boundary line?
E
test a point that is not on the boundary?
F
shade inside the parabola?

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