Name
Date
Class
Practice B
LESSON
9-9
The Quadratic Formula and the Discriminant
Solve using the quadratic formula.
1. x 2 ! x " 12
2. 4x 2 # 17x # 15 " 0
3
5, !__
4
3, !4
2
2
3. 2x # 5x " 3
4. 3x ! 14x # 5 " 0
1
3, !__
2
1 , !5
__
3
Find the number of real solutions of each equation using the discriminant.
5. x 2 ! 25 " 0
6. x 2 # 11x ! 28 " 0
no real solutions
7. x 2 ! 8x ! 16 " 0
2
1
Solve using any method.
8. x 2 ! 8x ! 15 " 0
9. x 2 # 49 " 0
7, !7
!3, !5
2
2
10. 6x ! x # 1 " 0
11. x ! 8x # 20 " 0
1
1 , !__
__
3
!10, 2
2
12. In the past, professional baseball was played at the Astrodome in
Houston, Texas. The Astrodome has a maximum height of 63.4 m.
The height of a baseball t seconds after it is hit straight up in the air
with a velocity of 45 ft/s is given by h " #9.8t 2 ! 45t ! 1. Will a
baseball hit straight up with this velocity hit the roof of the Astrodome?
Use the discriminant to explain your answer.
No;
the discriminant is negative so it will never reach the given height.
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