Download unit 12 foldable for class ink.notebook

unit 12 foldable for class ink.notebook
May 08, 2017
Solving Quadratic Equations
Solving Quadratic Equations
3x2 – 8 = 22
+8
+8
2
3x = 30
3
3
x2 = 10
x =+
- 10
1) get x2 by itself
Add or subtract
constant to each side
5(x + 1)2 = 80
5
5
1) get (x + 1)2 by itself
(x + 1)2 = 16
2) Take the square root of
each side
+4
x + 1 =-1 -1
+4
x = -1 -
multiply or divide
coefficient
2) Take the square
root of each side
-
1 + 4
x = 3
1 - 4
x = -5
-
multiply or divide
coefficient
3) get x by itself
Add or subtract
constant to each side
4) get 2 answers if
possible
Completing the Square
x + 6x – 16 = 0 + 16 + 16
1) move the constant to the x2 + 6x + ___ = 16 + ___ other side & add blanks
2
x + 6x + 9 = 16 + 9 6
2) Divide by 2 and square
2
it to fill in blanks
2
3 2 (x + 3) = 25
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Solve each equation. Recall that those with an x2 will have two solutions. A) 3x2 – 18 = 30
B) 5(x – 6)2 = 250
This is your squared binomial
(x + 3)2 = 25
x + 3 = ±5
-3
-3
x = -3 ± 5
-3 - 5
-3 + 5
x = 2 and x = –8
3) Take the square root of each side 4) add or subtract the
constant to the other
side and solve for x
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unit 12 foldable for class ink.notebook
Solve by completing the square. Show all work. Give the exact answer only. C) x2 – 8x = 20 Solve by completing the square. Show all work. Give the exact answer only. D) x2 + 6x + 4 = 10
Completing the Square - VERTEX FORM
f(x) = x2 – 10x + 5 – 5
– 5
1) move the constant to the –5 + ___ = x2 – 10x + ___ other side & add blanks
2
–
5 + 25 = x – 10x + 25 –10
2) Divide by 2 and square
it to fill in blanks
2
(–5)2
20 = (x – 5)2 -20
-20
3) add or subtract the
2 constant to the other
f(x) = (x – 5) – 20 Vertex: (5, –20)
May 08, 2017
Write each quadratic function in vertex form. Give the coordinates of the vertex and the axis of symmetry. Then tell whether the vertex is a maximum or a minimum. E) f(x) = x2 + 4x – 12 side
4) Put f(x) back it
Axis of symmetry: x = 5
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unit 12 foldable for class ink.notebook
Write each quadratic function in vertex form. Give the coordinates of the vertex and the axis of symmetry. Then tell whether the vertex is a maximum or a minimum. May 08, 2017
G) Create a quadratic equation that has solutions of –5 and 8. Leave in factored form. F) f(x) = x2 – 14x + 24 H) A package of supplies is dropped from a helicopter hovering 200 meters above the ground. The attached parachute fails to open. The equation h = –4.9t2 + 200 models this situation. After how many seconds will the package reach the ground? Round to the nearest hundredth.
The Discriminant
ax2 + bx + c = 0
(must = 0)
the discriminant = (b)2 - 4ac
if
(b)2 - 4ac > 0
(positive)
then 2 distinct real solutions
if
(b)2 - 4ac = 0
then 1 real solution or
a double root
if
(b)2 - 4ac < 0
(negative)
then 0 real solutions,
2 complex solutions (imaginary)
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unit 12 foldable for class ink.notebook
Find the discriminant and tell the number AND type of
solutions: I) 2x2 + 3x + 4 = 0
J) 9x 2 – 18x = –9
May 08, 2017
Find the discriminant and tell the number AND type of
solutions: K) 2x2 + 5x = 4
The Quadratic Formula
ax2 + bx + c = 0
(must = 0)
L) An athlete throws a shot put and the height can be modeled by the equation h = –16t2 + 29t + 6. Determine if it ever reaches a height of 20 ft. x =
– b ±
(b)2 - 4ac
2a
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unit 12 foldable for class ink.notebook
May 08, 2017
Solve the following by using the Quadratic formula. The Quadratic Formula
N)
M) 2x2 + 5x – 7 = 0
n2 + 4n = –1
2x2 – 11x = 21
2x2 – 11x – 21 = 0 (must = 0)
x =
–(–11) ±
x =
x =
(–11)2 - 4(2)(–21)
2(2)
11 ±
289
4
11 + 17
4
x = 7
=
11 ± 17
4
x =
11 – 17
4
x = –2
O) Julian kicked a soccer ball into the air with an initial upward
velocity of 40 feet per second. The height h in feet of the ball above the ground can be modeled by h = –16t2 + 40t + 1, where t is the time in seconds after Julian kicked the ball. What is the height of the ball after 1 second? Find the time it takes the ball to reach the ground. Round to nearest hundredth. Dropped in feet:
H =
landing height
in feet
Launched or thrown in feet:
– 16t2 + h0
time
in seconds
H=
– initial height
in feet
16t2 + v0t + h0
initial velocity
in feet/sec
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unit 12 foldable for class ink.notebook
May 08, 2017
Q) The length of a rectangle is 9 more than the width. Write an expression for the area of the rectangle.
P) A tennis ball is dropped from a height of 213 feet. How long does it take for the ball to hit the ground? The area is 90 square centimeters. Find the dimensions of it.
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