1.7 Complete the Square
A Solve the equation by finding square roots.
x2 + 2x + 1 = 9
x2 + 6x + 9 = 1
x2  4x + 4 = 16
x2  l0 + 25 = 4
x2  14x + 49 = 7
x2 + 20x + 100 = 12
1
1
7. x2  x+
4
8. 2x2 + 16x + 32 = 14
9. 4x2 + 12x + 9 = 16
Find the value of c hat makes the expression a perfect
square trinomial. Then write the expression as a
square of a binomial.
1.
2.
3.
4.
5.
6.
10. x2 + 4x + c
11. x2  2x+ c
12. x2 + 18x c
13. x2 + 24x+ c
14. x2  14x+ c
15. x2  5x c
16. x2 + x + c
17. x2 + 7x c
Solve the equation by completing the square.
18. x2  2x  2 = 0
19. x2 + 6x + 3 = 0
20. x2 +8x  2= 0
21. x2 +2x +5= 0
22. x2 + 10x + 11 = 0
23. x2  14x + 10 = 0
24. x2  x +1= 0
25. x2  x  3= 0
Write the quadratic function in vertex form. Then
identify the vertex.
26. .y = x2 + 8x + 5
27. y = x2  12x + 1
28. y = x2 + 4x + 12
29. y = x2  10x + 3
Find the value of x.
30.
31.
32. Area of rectangle = 40
33. Area of rectangle = 78
34. Area of triangle = 16
35. Area of triangle = 40
B Solve the equation by finding square roots.
x2 + 8x+16 = 9
x26x + 9 = 25
x2  12x + 36 = 49
2x2  12x + 18 = 32
4x2  4x + 1 = 36
5x2  20x + 20 = 35
1
2
7. x2  x +
=1
9
3
8. x2 + 3 x + =93
2
16
9. 9x2 + 12x + 4 = 5
1.
2.
3.
4.
5.
6.
Find the value of c that makes the expression a
perfect square trinomial. Then write the
expression as a square of a binomial.
10.
11.
12.
13.
14.
15.
x2 + 8x + c
x2  22x + c
x2 + 16x + c
x2 + 3x + c
x2  9x + c
9x2  12x + c
Find the value of x.
Solve the equation by completing the square.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
x2 + 4x = 1
x210x= 10
x2  2x  9 = 0
x2 + 6x + 10 = 0
x2 + 8x + 4 = 0
3x2 + 36x = 42
x224x+81 = 0
4x2 + 20x + 25 = 0
3x2  3x + 9 = 0
6x2  12x  18 = 0
Write the quadratic function in vertex form. Then
identify the vertex.
26.
27.
28.
29.
y=x2+14x+11
y = x2  8x + 10
y = 2x2 + 4x – 5
y = 3x2  9x + 18
30. Area of rectangle = 84
31. Area of triangle = 20
Shot Put In a track and field event, a contestant
had a throw in the shot put that can be modeled by
y =  0.02x2 + x + 6 where x is the shot put’s
horizontal distance & (in feet) and y is the
corresponding height (in feet). How long was the
throw? Round the answer to the nearest tenth
1.8 Use the Quadratic Formula and the Discriminant
B. Find the discriminant of the quadratic equation.
1.
2.
3.
4.
5.
x2  3x + 5 = 0
2x2 + x + 2 = 0
4x2  9x + 2 = 0
3x2 + 6x  3 = 0
3x2 + 3x  1 = 0
6. 7x2  4x + 5 = 0
Find the discriminant and use it to determine if the solution has one real, two real, or two imaginary solution(s).
x2 + 4x + 3 = 0
x2  2x + 4 = 0
x2  2x + 1 = 0
3x2 + 2x  1 = 0
 x2  x = 4
5x2  4x + 1 = 3x + 4
Use the quadratic formula to solve the equation.
7.
8.
9.
10.
11.
12.
13. x2 + 4x  2 = 0
14. 2x2 5x  2 = 0
15. x2 + 2x = 4x
16. 6x2 + 3x + 2 = 3
17. x2 + 1 = 5x2 + 4x
18. 2(x  3)2 = 2x + 9
19. 2.5x2  2.8x = 0.4
20. 4.8x2 = 5.2x + 2.7
Solve the equation using the quadratic formula. Then solve the equation by factoring to check your solution(s).
21. x2  2x  24 = 0
22. x2  2x + 1 = 0
23. 2x2  9x + 9 = 0
24. 6x2 + 17x + 5 = 0
25. 10x2 + x = 2
26. 6x2 = 5x + 6
27. New Carpet You have new carpeting installed in a rectangular room. You are charged for 28 square yards of
carpet and 60 feet (20 yards) of tack strip. Tack strip is used along the perimeter to secure the carpet in place. Do
you think these figures are correct? Explain your answer.
In Exercises 2831, use the following information. Launched Object An object is launched upward with an initial
velocity of 64 feet per second from a platform 80 feet high.
28.
29.
30.
31.
Write a height model for the object.
How many seconds until the maximum height is reached?
What will be the maximum height?
How many seconds until the object hits the ground?