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SWBAT: solve quadratic equations using the quadratic formula.
SWBAT: solve quadratic equations using the quadratic formula.
x2 + 8x + y2 – 4y = -14
Magic number for x: 𝟖
𝟐
𝟐= 𝟏𝟔
Magic number for y: −𝟒
𝟐
𝟐= 𝟒
(x + 4)2 + (y - 2)2 = 6 Center = (-4, 2)
r = 𝟔 ≈ 𝟐. 𝟒
x2 + 8x + 16 + y2 – 4y + 4 = -14 + 16 + 4
SWBAT: solve quadratic equations using the quadratic formula.
2 ax2 + bx + c = 0
0
Factoring
decimal 𝒏𝒐𝒏 − 𝒑𝒆𝒓𝒇𝒆𝒄𝒕 𝒔𝒒𝒖𝒂𝒓𝒆 #
−𝒃 ± 𝒃𝟐 − 𝟒𝒂𝒄
𝟐𝒂
SWBAT: solve quadratic equations using the quadratic formula.
No 2x2 - 4x - 1 = 0
2 -4 -1
x = − ± ( )𝟐−𝟒( )( )
𝟐( )
x = − −𝟒 ± (−𝟒)𝟐−𝟒(𝟐)(−𝟏)
𝟐(𝟐)
x = 𝟒 ± 𝟐𝟒
𝟒
𝟒 ± 𝟒 𝟔
𝟒
x = 𝟒 ± 𝟐 𝟔
𝟒
GCF = 2 Divide all whole numbers by 2
x = 𝟐 ± 𝟔
𝟐
SWBAT: solve quadratic equations using the quadratic formula.
SWBAT: solve quadratic equations using the quadratic formula.
3x2 + 12x - 3 = 0
a =
b =
c =
3
12
-3
x = − ± ( )𝟐−𝟒( )( )
𝟐( )
x = − 𝟏𝟐 ± (𝟏𝟐)𝟐−𝟒(𝟑)(−𝟑)
𝟐(𝟑)
x = −𝟏𝟐 ± 𝟏𝟖𝟎
𝟔
−𝟏𝟐 ± 𝟑𝟔 𝟓
𝟔
x = −𝟏𝟐 ± 𝟔 𝟓
𝟔
x = -2 ± 𝟓
GCF = 6 Divide all whole numbers by 6
SWBAT: solve quadratic equations using the quadratic formula.
x2 - 6x - 12 = 0
a =
b =
c =
1
-6
-12
x = − ± ( )𝟐−𝟒( )( )
𝟐( )
x = − −𝟔 ± (−𝟔)𝟐−𝟒(𝟏)(−𝟏𝟐)
𝟐(𝟏)
x = 𝟔 ± 𝟖𝟒
𝟐
𝟔 ± 𝟒 𝟐𝟏
𝟐
x = 𝟔 ± 𝟐 𝟐𝟏
𝟐
x = 3 ± 𝟐𝟏
GCF = 2 Divide all whole numbers by 2
SWBAT: solve quadratic equations using the quadratic formula.
7x2 + 4x + 8 = 0
a =
b =
c =
7
4
8
x = − ± ( )𝟐−𝟒( )( )
𝟐( )
x = − 𝟒 ± (𝟒)𝟐−𝟒(𝟕)(𝟖)
𝟐(𝟕)
x = −𝟒 ± −𝟐𝟎𝟖
𝟏𝟒
No Real Solution
SWBAT: solve quadratic equations using the quadratic formula.
x2 + 3x - 4 = 0
a =
b =
c =
1
3
-4
x = − ± ( )𝟐−𝟒( )( )
𝟐( )
x = − 𝟑 ± (𝟑)𝟐−𝟒(𝟏)(−𝟒)
𝟐(𝟏)
x = −𝟑 ± 𝟐𝟓
𝟐
−𝟑 ± 𝟓
𝟐
x = −𝟑 − 𝟓
𝟐 or x =
−𝟑 + 𝟓
𝟐 {-4, 1}
x = −𝟖
𝟐 or x =
𝟐
𝟐
SWBAT: solve quadratic equations using the quadratic formula.
SWBAT: solve quadratic equations using the quadratic formula.
–12t2 + 54t = 0
a =
b =
c =
-12
54
0
t = − ± ( )𝟐−𝟒( )( )
𝟐( )
t = − 𝟓𝟒 ± (𝟓𝟒)𝟐−𝟒(−𝟏𝟐)(𝟎)
𝟐(−𝟏𝟐)
t = −𝟓𝟒 ± 𝟐𝟗𝟏𝟔
−𝟐𝟒
−𝟓𝟒 ± 𝟓𝟒
−𝟐𝟒
t = −𝟓𝟒 − 𝟓𝟒
−𝟐𝟒 or t =
−𝟓𝟒 + 𝟓𝟒
−𝟐𝟒
t = −𝟏𝟎𝟖
−𝟐𝟒 or t =
𝟎
−𝟐𝟒
t = 4.5 sec
SWBAT: solve quadratic equations using the quadratic formula.
a =
b =
c =
-5
-8
120
t = − ± ( )𝟐−𝟒( )( )
𝟐( )
t = − −𝟖 ± (−𝟖)𝟐−𝟒(−𝟓)(𝟏𝟐𝟎)
𝟐(−𝟓)
t = 𝟖 ± 𝟐𝟒𝟔𝟒
−𝟏𝟎
𝟖 ± 𝟒𝟗.𝟔𝟑𝟖𝟕…
−𝟏𝟎
t = 𝟖 −𝟒𝟗.𝟔𝟑𝟖𝟕…
−𝟏𝟎 or t =
𝟖 + 𝟒𝟗.𝟔𝟑𝟖𝟕…
−𝟏𝟎
t 𝟒. 𝟐 𝒔𝒆𝒄 or t −𝟓. 𝟖 𝒔𝒆𝒄
SWBAT: solve quadratic equations using the quadratic formula.
a =
b =
c =
-16
200
0
Determine Maximum Height
x = -𝒃
𝟐𝒂 =
−( )
𝟐( )
= −( 𝟐𝟎𝟎)
𝟐(−𝟏𝟔)
t = −𝟐𝟎𝟎
−𝟑𝟐 =
𝟐𝟓
𝟒
𝑯𝒎𝒂𝒙 =-16(𝟐𝟓
𝟒)2 + 200(
𝟐𝟓
𝟒)
𝑯𝒎𝒂𝒙 = 625 ft
𝟔𝟐𝟓 > 𝟔𝟏𝟐; 𝒀𝒆𝒔 𝒉𝒆 𝒘𝒊𝒍𝒍!
SWBAT: solve quadratic equations using the quadratic formula.
a =
b =
c =
-4.9
68.6
0
Determine Maximum Height
x = -𝒃
𝟐𝒂 =
−( )
𝟐( )
= −( 𝟔𝟖.𝟔)
𝟐(−𝟒.𝟗)
t = −𝟔𝟖.𝟔
−𝟗.𝟖= 𝟕
𝑯𝒎𝒂𝒙 =-4.9(𝟕)2 + 68.6(𝟕)
𝑯𝒎𝒂𝒙 ≈ 240 meters
SWBAT: solve quadratic equations using the quadratic formula.
SWBAT: solve quadratic equations using the quadratic formula.
5a2 – 2a – 22 = 0 a =
b =
c =
5
-2
-22
a = − −𝟐 ± (−𝟐)𝟐−𝟒(𝟓)(−𝟐𝟐)
𝟐(𝟓)
a = 𝟐 ± 𝟒𝟒𝟒
𝟏𝟎
𝟐 ± 𝟒 𝟏𝟏𝟏
𝟏𝟎
a = 𝟐 ± 𝟐 𝟏𝟏𝟏
𝟏𝟎 GCF = 2 Divide all whole
numbers by 2
a = 𝟏 ± 𝟏𝟏𝟏
𝟓