Download Solving Quadratic Equations By Graphing: First find the axis of symmetry:

Solving Quadratic Equations
By Graphing:
b
2a
Solve each of the equations by graphing:
1. x2 − 4x + 3 = 0
2. x2 − 4x = 5
3. x2 + 2x = 0
First find the axis of symmetry: x 
4. x2 − 9 = 0
5. x2 + 2 = 3x
6. x2 − 7x + 12 = 0
7. x2 − 4x + 4 = 0
8. x2 + 6x + 9 = 0
9. 2x2 + x − 1 = 0
10. x2 − 3x + 1 = 0
11. x2 − x = 3
12. x2 − 2 = 0
13. x2 − 2x − 1 = 0
14. x2 + 2x − 2 = 0
15. x2 − 4x + 2 = 0
16. x2 − x − 4 = 0
Completing the Square:
1
Must be 1x2 ; Take the coefficient of x ; Square the result.
2
Complete the square for each of the following:
1. x2 + 12 x + ____ 2. x2 − 8x + ____
3. x2 + 4x + ____
4. x2 − 6x + ____
5. x2 + 10x + ____
6. x2 − 14x + ____
7. x2 + 16x + ____
8. x2 − 18x + ____
9. y2 + 5y + ____
10. x2 − x + ____
11. a2 +
17. 2x2 + 4x − 5 = 0 18. 3x2 − 3x − 1 = 0
1
a + ____
2
12. x2 − 2x + ____
Solve each of the equations by taking the square root of both sides of the equation:
1. x2 =16
2. x2 = 25
3. x2 = 121
4. x2 = 64
5. (x −3)2 = 9
6. (x + 5)2 = 4
7. (x − 2)2 = 49
8. (x + 7)2 = 1
9. x2 = −81
10. x2 = − 36
11. (x + 3)2 = −25
12. x2 = − 48
Solve each equation by completing the square:
1. x2 + 4x + 3 = 0
2. x2 − 2x = 15
3. y2 = 9 + 8y
4. a2 + 5 = 6a
5. x2 − 3x + 2 = 0
8. 3y = y2 − 4
6. x2 − x = 20
9. 4x2 − 8x − 21 = 0 10. 2t2 + 5t + 3 = 0
7. x2 − 5x = 14
11. x + 2 =
3
x
12.
4
5 6
 
x3 2 x