5-1 - mathppt.com · y =ax2 +bx+c Quadratic Equation Quadratic Term Constant Term Objective - To...
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y = ax 2 + bx + c Quadratic Equation Quadratic T erm Constant T erm Objective - To transform quadratic functions. a +a opens up -a opens down skinny parabola a > 1 wide parabola 0 < a < 1 c +c shifts up -c shifts down y-intercept y Graph f ( x ) = x 2 x y -3 2 9 4 x -2 -1 0 1 2 3 4 1 0 1 4 9 Vertex (0,0) Axis of Symmetry x = 0 y Graph f ( x ) = x 2 − 5 x y -3 -2 1 −3 ( ) 2 − 5 = 4 −2 ( ) 2 − 5 =−1 1 ( ) 2 5 4 x -1 0 1 2 3 Vertex (0,-5) Axis of Symmetry x = 0 −1 ( ) − 5 =−4 0 () 2 − 5 =−5 1 () 2 − 5 =−4 2 () 2 − 5 =−1 3 () 2 − 5 = 4 y Graph f ( x ) =− x 2 + 4 x y -3 -2 1 Vertex (0,4) Axis of Symmetry x = 0 −−3 ( ) 2 + 4 = −5 −−2 ( ) 2 + 4 = 0 1 ( ) 2 + 4 3 x -1 0 1 2 3 − −1 ( ) + 4 = 3 − 0 ( ) 2 + 4 = 4 − 1 ( ) 2 + 4 = 3 − 2 ( ) 2 + 4 = 0 − 3 ( ) 2 + 4 = −5 Translations of Quadratic Functions y Horizontal Translation 2 ( ) ( ) f x h h x f ( x ) = x 2 x ( ) ( ) − = − f x h h x h < 0 moves left h > 0 moves right Translations of Quadratic Functions y Vertical Translation 2 () + k fx x k f ( x ) = x 2 x () − = + k fx x k k < 0 moves down k > 0 moves up Lesson 5-1 Algebra 2 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2010
Transcript of 5-1 - mathppt.com · y =ax2 +bx+c Quadratic Equation Quadratic Term Constant Term Objective - To...
y = ax2 + bx + cQuadratic Equation
QuadraticTerm
ConstantTerm
Objective - To transform quadratic functions.
e ea
+a opens up-a opens down
skinny parabola a >1
wide parabola0< a <1
c
+c shifts up-c shifts down
y-intercept
yGraph f (x) = x2
x y
-32
94
x
-2-10123
410149
Vertex(0,0)Axis of
Symmetryx = 0
y
Graph f (x) = x2 − 5
x y
-3-21
−3( )2 − 5 = 4−2( )2 − 5 = −1
1( )2 5 4x
-10123
Vertex(0,-5)
Axis ofSymmetry
x = 0
−1( ) − 5 = −40( )2 − 5 = −51( )2 − 5 = −42( )2 − 5 = −13( )2 − 5 = 4
y
Graph f (x) = −x2 + 4
x y
-3-21
Vertex(0,4)
Axis ofSymmetry
x = 0− −3( )2 + 4 = −5− −2( )2 + 4 = 0
1( )2 + 4 3x
-10123
− −1( ) + 4 = 3− 0( )2 + 4 = 4− 1( )2 + 4 = 3− 2( )2 + 4 = 0− 3( )2 + 4 = −5
Translations of Quadratic Functions
y
Horizontal Translation
2( ) ( )f xh hx
f (x) = x2
x( ) ( )− = −f xh hx
h < 0 moves left
h > 0 moves right
Translations of Quadratic Functions
y
Vertical Translation
2( ) +kf x x k
f (x) = x2
x
( ) − = +kf x x k
k < 0 moves down
k > 0 moves up
Lesson 5-1
Algebra 2 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2010
Translations of Quadratic Functions
y
Reflection
f (x) = x2
f (x) = x2
x
− f (x) = −x
Stretches and Compressions
y
Horizontal Stretch
f (x) = x2
2
x2
21 1⎛ ⎞ ⎛ ⎞=⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
xb
f xb
b > 1 stretches
0 < b < 1 compresses
Stretches and Compressions
y
Horizontal Compression
f (x) = x2
x ( )2 2• =f xa ax
a > 1 stretches
0 < a < 1 compresses
y = a(x − h)2 + k
Vertex Form of a Quadratic Equation
vertex (h,k)axis of symmetry x = h
Lesson 5-1 (cont.)
Algebra 2 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2010
