Name: ____________
Date: ____________
Quadratic Equations
Solve each equation. x2 + ax + b = c
1.
x2 + 6x + 9 = 16
2.
x2 - 4x + 4 = 25
(x + 3)2 = 16
x+3=±4
x=±4-3
x = -7, 1
3.
5.
7.
9.
Page 10
x2 - 6x + 9 = 36
x2 - 10x + 25 = 16
x2 - 12x + 36 = 81
x2 - 14x + 49 = 100
4.
6.
8.
10.
x2 + 8x + 16 = 49
x2 + 4x + 4 = 64
x2 - 8x + 16 = 25
x2 + 16x + 64 = 36
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Name: ____________
Date: ____________
Quadratic Equations
Solve each equation using the FOIL method.
x2 + 2x - 3 = 0
1.
1
1
1
-1
+3
2.
x2 - x - 20 = 0
-3
3-1=2
(x - 1)(x + 3) = 0
x = -3, 1
3.
x2 - 8x + 12 = 0
4.
x2 - 2x - 63 = 0
5.
x2 - 9x + 14 = 0
6.
x2 - 9x - 22 = 0
7.
x2 - 14x + 48 = 0
8.
x2 - 12x + 27 = 0
9.
x2 - 6x - 40 = 0
10.
x2 - 6x + 5 = 0
Page 21
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Name: ____________
Date: ____________
Quadratic Equations
Answer the following questions based on the graphs on previous 5 pages.
From
To
Result
y = x2
y = -x2
parabola turns upside down
y = x2
y = (x - 3)2
axis of symmetry moves from x = 0 to x = ___
y = (x - 3)2
y = -(x - 3)2
parabola turns ________________
y = (x - 3)2
y = (x - 3)2 + 1
parabola moves ______ (up or down) by
1
2
3
4
_______ (number of units)
5
y = x2
y = 2x2
Parabola becomes _____________ (wider or
narrower)
6
y = x2
y = (1/3)x2
Parabola becomes _____________ (wider or
narrower)
7
y = (1/3)x2
y = (1/3)(x - 5)2
axis of symmetry moves from x = _____ to x =
_____
8
y = -(x - 1)2
y = -(x - 1)2 - 3
parabola moves ______ (up or down) by
_______ (number of units)
Page 62
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Name: ____________
Date: ____________
Quadratic Equations
Graphing by finding and using the axis of symmetry and vertex.
1.
x = y2 + 2y + 5
2.
x = y2 + 4y + 10
Completing the square:
x = y2 + 2y + 1 + 4
= (y + 1)2 + 4
axis of symmetry: y = -1
3.
x = 4y2 + 8y - 3
axis of symmetry:
5.
axis of symmetry:
4.
vertex =
x = -2y2 - 4y + 7
axis of symmetry:
Page 89
vertex = (4, -1)
vertex =
x = -y2 + 4
axis of symmetry:
6.
vertex =
vertex =
x = 3y2 + 12y + 5
axis of symmetry:
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vertex =
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Name: ____________
Date: ____________
Quadratic Equations
Determine the quadratic equation of the graph.
1.
2.
2
-4
2
-5
y=
3.
1
(x - 2) 2
2
x=4
4.
x = -2
1
6
-3
Page 108
(-5, -4)
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Name: ____________
Date: ____________
Quadratic Equations
Graph Inequality
Example :
y  (x + 2)2 - 4
try point (-2, 0): 0  (-2 + 2) - 4
0  -4, this is true.
Therefore, the answer is the shaded area inside the parabola.
Since the answer includes the parabola itself, solid line is used for the curve.
y = (x + 2)2 - 4
(-2, 0)
Example :
y < x2 - 8x + 12
y < x2 - 8x + 16 - 4
y < (x - 4)2 - 4
try point (4, 0): 0 < (4 - 4)2 - 4
0 < -4, this is NOT true.
Therefore, the answer is the shaded area outside the parabola.
Since the answer doesn’t include the parabola itself, dotted line is used.
y = (x - 4)2 - 4
(4, 0)
Page 114
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