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Solve each equation.
1.
 6x2 - 864 = 0

 2 -3x2 + 300 = 0
3.
-8
 2 5
x2 +
58
 4 5
=
8
 2 5

Solve each equation by factoring.
4.
1
 1 2
x2 + 120  =  -27x

5.
 -6x2 - 14x + 33 = -7x2

6.
-2
 1 3
x2 +
 1 3
=
-2
 1 2
x2 +
 1 2
x

Solve each equation by completing the square.
7.
 -3x2 - 36x - 21 = 0

 8 5x2 - 9x + 4 = 0
9.
-3
 1 3
x2 +
1
 2 3
x  =
1
 1 3
x -
 2 3

Use the discriminant to determine the nature of each quadratic equation's roots.
 10 9x2 + 12x + 4 = 0
11.
4
 1 2
x2 + 6x + 2  =  0

12.
8
 1 3
x2 + 50x -
8
 1 3
=  25

Use the quadratic formula to solve each equation.
13.
24
 3 4
x2 -
82
 1 2
x  =  -33

 14 -5x2 + 12x - 7 = 0
15.
 -36x + 16 = -20x2

Use the quadratic formula to solve each equation.
16.
 -10x2 + 6x - 2 = -5x2

17.
27
 1 2
x2 + 10x +
7
 1 2
=  0

18.
 -5x + 8 = -10x2 + 6

Write a quadratic equation that has the given roots.
19.
 { 2 , -5 }

20.
 { 4 , 2 }

21.
 -2 2i

Find the vertex and axis of symmetry of the parabola.
 22 -12x2 - 5x + 12 = 0
 23 -4x2 + 2x + 11 = 0
 24 3x2 + 7x + 2 = 0

Find the vertex and axis of symmetry of the parabola.
25.
 y = -x2 - 5x + 12

26.
 y = 36x2 - 12x - 8

27.
y  =  3x2 - 6x -
 3 4

Write an equation for a parabola that passes through the given points.
 28 (6, 27), (5, 18), (-4, 27), (-3, 18)

Graph each equation.
 29 y = x2 - 10x + 19
 30 y = -x2 + 2x + 2

Solve each inequality.
 31 x2 + 3x + 2 0
 32 -8x2 - 10x + 3  <  0
 33 5x2 - x - 4  >  0

Sample
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