WORKSHEET 9-5
Algebra 1
Name ________________________________________
Class Hour __________
Directions: Short Answer
1. Does the discriminant give the exact roots of a quadratic equation (The points
where the parabola crosses the x-axis)?
2. How is the discriminant related to the quadratic formula?
3. Explain WHY…
a. If b2 – 4ac > 0 WHY are there 2 roots?
b. If b2 – 4ac = 0 WHY is there only 1 root?
c. If b2 – 4ac < 0 WHY are there no roots?
Directions: 1) Find the Discriminant (b2 – 4ac)
2) Determine the number of the roots (2 roots, 1 root or NO roots)
3) Use the Quadratic formula to find the EXACT Roots (
4. x2 + 3x – 4 = 0
a = _____
b ± b2
2a
4ac
)
5. 2x2 + 4x + 1 = 0
b = _____
c = _____
a = _____
b = _____
c = _____
Discriminant:
Discriminant:
Number of Roots: ___________________
Number of Roots: ___________________
Quadratic Formula:
Quadratic Formula:
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Directions: 1) Find the Discriminant (b2 – 4ac)
2) Determine the number of the roots (2 roots, 1 root or NO roots)
3) Use the Quadratic formula to find the EXACT Roots (
6. 5x2 – 3 = 0
a = _____
b ± b2
2a
4ac
)
7. 3x2 – 10x
b = _____
c = _____
a = _____
b = _____
c = _____
Discriminant:
Discriminant:
Number of Roots: ___________________
Number of Roots: ___________________
Quadratic Formula:
Quadratic Formula:
8. 2x2 + 7x + 50 = 0
9. 4x2 – 5x = 11
a = _____
b = _____
c = _____
a = _____
b = _____
c = _____
Discriminant:
Discriminant:
Number of Roots: ___________________
Number of Roots: ___________________
Quadratic Formula:
Quadratic Formula:
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Directions: Find the Roots using the method indicated. (HINT: Begin by solving for "y")
10. GRAPH: y – 5 = x2 + 6x + 3
D:
W.
A:
V:
R:
11. FACTOR: y – 5 = x2 + 6x + 3
12. COMPLETE THE SQUARE:
y – 5 = x2 + 6x + 3
13. USE THE QUADRATIC FORMULA:
y – 5 = x2 + 6x + 3
Disc:
# of Roots: _______________
Quad Formula:
14. Did you get the same “answer” for 10 – 13? _________ Should you have? ____________
Why or Why Not??
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