4-2 Quadratic Functions: Standard Form Today’s Objective: I can graph a quadratic function in...
-
Upload
terence-tyler -
Category
Documents
-
view
212 -
download
0
Transcript of 4-2 Quadratic Functions: Standard Form Today’s Objective: I can graph a quadratic function in...
4-2 Quadratic Functions:
Standard Form
Today’s Objective:
I can graph a quadratic function in standard form
The function models the height h of the soccer ball as it travels distance x. What is the maximum height of the ball? Explain.
h=− 0.01 ( 45 )2+0.9(45)¿20.25 𝑓𝑡
x
y
Quadratic Function: Vertex Form𝑓 (𝑥)=±𝑎(𝑥− h)2+𝑘 Attributes:
• Opens up (a > 0) or down (a < 0)• Vertex is maximum or minimum• Vertex: (h, k)• Axis of symmetry:
x
y
(h ,𝑘)
𝑥=h
Quadratic Function: Standard FormAttributes:• Opens up (a > 0) or down (a < 0)• Vertex is maximum or minimum• y-intercept: (0, c)
Can be determined with a little work• Axis of symmetry: • Vertex:
𝑓 (𝑥)=𝑎𝑥2+𝑏𝑥+𝑐
x
y
x
y
x
y
x
y
(0, c)
𝑥=−𝑏2𝑎
(−𝑏2𝑎
, 𝑓 (−𝑏2𝑎 ))
Evaluate f(x) at
Graphing a Quadratic Function: Standard form1. Plot the vertex2. Find and plot two points
to the right of vertex. 3. Plot the point across axis
of symmetry.4. Sketch the curve.
Vertex:
Axis of Symmetry:Domain:
Range:
All Real Numbers
𝑦=𝑥2+2𝑥+3
Units right of vertex
x
Units up from
vertex
1
2
14𝑦 ≥ 2
𝑥2
𝑥=−1
𝑥=−𝑏2𝑎¿
−22(1)¿−1
𝑦=(−1)2+2 (−1 )+3
¿2
(−𝟏 ,𝟐)
-5 5
-2
8
x
y
x
y
x
y
x
y
Graphing a Quadratic Function: Standard form1. Plot the vertex2. Find and plot two points
to the right of vertex. 3. Plot the point across axis
of symmetry.4. Sketch the curve.
Vertex:
Axis of Symmetry:Domain:
Range:
All Real Numbers
𝑦=2 𝑥2− 4 𝑥−5
Units right of vertex
x
Units up from
vertex
1
2
28𝑦 ≥ −7
2
𝑥=1
𝑥=−𝑏2𝑎¿
42(2)¿1
𝑦=2(1)2 − 4 (1 ) −5
¿−7
(𝟏 ,−𝟕)
-5 5
-8
2
x
y
x
y
x
y
x
y
Graphing a Quadratic Function: Standard formVertex:
Axis of Symmetry:Domain:
Range:
All Real Numbers
𝑦=− 0.5𝑥2+2 𝑥−3
Units right of vertex
x
Units up from
vertex
1
2
− 0.5−2
𝑦 ≤ −1
-0.5
𝑥=2𝑥=
−𝑏2𝑎¿
− 22(− .5)¿2
𝑦=− 0.5 (2 )2+2 (2 ) −3
¿−1
(𝟐 ,−𝟏)
-5 5
-8
2
x
y
x
y
x
y
x
y
Vertex on Calculator:[2nd], [trace]Choose minimum or maximumMove curser left of vertex, [enter]Move curser right of vertex, [enter][enter]
Standard form to Vertex form
𝑦=±𝑎(𝑥− h)2+𝑘𝑦=𝑎𝑥2+𝑏𝑥+𝑐• a value is the same• Find the vertex
𝑦=2 𝑥2+10 𝑥+7
𝑥=−102(2)¿− 2.5
𝑦=2(−2.5)2+10 (−2.5 )+7¿−5.5
𝑦=2(𝑥+2.5)2 −5.5
𝑦=−𝑥2+4 𝑥−5
𝑥=− 4
2(−1)¿2
𝑦=− (2 )2+4 (2 )− 5¿−1
𝑦=−(𝑥− 2)2 −1
Bungee JumpingYou can model the arch of this bridge with the function How high above the river is the arch?
x
y
x
y Maximum
𝑥=− 0.847
2(− 0.000498)¿850
𝑦=− 0.000498 (850 )2+0.847(850)¿360
(850,360)Arch height:516+360¿876 𝑓𝑡
p.206:8-30 evens