Notes Over 9.7Using the Discriminant

The discriminant is the expression under the radical:

b ac2 4If it is Positive:Then there are Two Solutions

If it is Zero:Then there is One Solution

If it is Negative:Then there is No Solution

b a c2 4 b gb g

Notes Over 9.7Finding the Number of SolutionsFinding the Number of Solutions

02510 1 2 xx.

100

Tell if the equation has two solutions, one solution, or no solution.

10 1 25

1000

b a c2 4 b gb g

Notes Over 9.7Finding the Number of SolutionsFinding the Number of Solutions

012 2 2 xx.

1

Tell if the equation has two solutions, one solution, or no solution.

1 2 18

9

b a c2 4 b gb g

Notes Over 9.7Finding the Number of SolutionsFinding the Number of Solutions

042 3 2 xx.

4

Tell if the equation has two solutions, one solution, or no solution.

2 1 4

1612

b a c2 4 b gb g

Notes Over 9.7Finding the Number of SolutionsFinding the Number of Solutions

096 4 2 xx.

36

Tell if the equation has two solutions, one solution, or no solution.

6 1 936

0

b a c2 4 b gb g

Notes Over 9.7Finding the Number of SolutionsFinding the Number of Solutions

0452 5 2 xx.

25

Tell if the equation has two solutions, one solution, or no solution.

5 2 4327

b a c2 4 b gb g

Notes Over 9.7Finding the Number of SolutionsFinding the Number of Solutions

01623 6 2 xx.

4

Tell if the equation has two solutions, one solution, or no solution.

2 3 16192

196

b a c2 4 b gb g

Notes Over 9.7Finding the Number of Finding the Number of xx-Intercepts-Intercepts

168 .7 2 xxy

64

Determine whether the graph of the function will intersect the x-axis in zero, one , or two points.

8 1 16

640

b a c2 4 b gb g

Notes Over 9.7Finding the Number of Finding the Number of xx-Intercepts-Intercepts

18 .8 2 xxy

64

Determine whether the graph of the function will intersect the x-axis in zero, one , or two points.

8 1 1

468

b a c2 4 b gb g

Notes Over 9.7Finding the Number of Finding the Number of xx-Intercepts-Intercepts

188 .9 2 xxy

64

Determine whether the graph of the function will intersect the x-axis in zero, one , or two points.

8 1 18

728

b a c2 4 b gb g

Notes Over 9.7Finding the Number of Finding the Number of xx-Intercepts-Intercepts

362 .10 2 xxy

36

Determine whether the graph of the function will intersect the x-axis in zero, one , or two points.

6 2 3

2412

b a c2 4 b gb g

Notes Over 9.7Finding the Number of Finding the Number of xx-Intercepts-Intercepts

85 .11 2 xxy

25

Determine whether the graph of the function will intersect the x-axis in zero, one , or two points.

5 1 832

7

b a c2 4 b gb g

Notes Over 9.7Finding the Number of Finding the Number of xx-Intercepts-Intercepts

9124 .12 2 xxy

144

Determine whether the graph of the function will intersect the x-axis in zero, one , or two points.

12 4 9

1440

Notes Over 9.7