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Name _____________________________
Date ___________________

Quadratic Equations and Parabolas
(Answer ID # 0363396)
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

 

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