notes over 9.7
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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
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