Download - 9.1: QUADRATIC GRAPHS:
9.1: QUADRATIC GRAPHS:
Quadratic Function: A function that can be written in the form y = ax2+bx+c where a ≠ 0.
Standard Form of a Quadratic: A function written in descending degree order, that is ax2+bx+c.
Quadratic Parent Graph: The simplest quadratic function f(x) = x2.
Parabola: The graph of the function f(x) = x2.
Axis of Symmetry: The line that divide the parabola into two identical halves
Vertex: The highest or lowest point of the parabola.
Minimum: The lowest point of the parabola.
Maximum: The highest point of the parabola. Line of Symmetry
Vertex = Minimum
GOAL:
IDENTIFYING THE VERTEX: The vertex will always be the lowest or the highest point of the parabola.
Ex: What are the coordinates of the vertex?
1) 2)
SOLUTION: The vertex will always be the lowest or the highest point of the parabola.
Vertex: ( 0, 3)
x =0 Line of Symmetry, y =3 is the Maximum
SOLUTION: The vertex will always be the lowest or the highest point of the parabola.
Vertex: ( -2, -3)
x = -2 Line of Symmetry, y = -3 is the Minimum
GRAPHING y = ax2: Remember that when we do not know what something looks like, we always go back to our tables.Ex: Graph y = x2. Make a table and provide the Domain and Range.
GRAPHING:X y = (1/3)x2 y
-2 (1/3) (-2)∙ 2 = 𝟒𝟑
(1/3) (-1)∙ 2 = 𝟏𝟑-1
0 (1/3) (0)∙ 2 0 = 0
1 (1/3) (1)∙ 2 𝟏𝟑=
2 (1/3) (2)∙ 2 =
GRAPHING: X y-2
-1
0
1
2
Domain (-∞, ∞)
𝟒𝟑𝟏𝟑
0 𝟏𝟑
Range: (0, ∞)
USING TECHNOLOGY: What is the difference and Similarities of :
1) y = x2
2) y = 4x2 3) y = -4x2
4) y = x2 5) y = - x2
USING TECHNOLOGY:
y = x2
Graphing calculators can aid us on looking at properties of functions:
Vertex: (0,0)
Domain: (- ∞, ∞)
Range: (0, ∞)
USING TECHNOLOGY:
y = 4x2
Graphing calculators can aid us on looking at properties of functions:
Vertex: (0,0)
Domain: (- ∞, ∞)
Range: (0, ∞)
USING TECHNOLOGY:
y = -4x2
Graphing calculators can aid us on looking at properties of functions:
Vertex: (0,0)
Domain: (- ∞, ∞)
Range: (- ∞, 0)
USING TECHNOLOGY:
y = x2
Graphing calculators can aid us on looking at properties of functions:
Vertex: (0,0)
Domain: (- ∞, ∞)
Range: (0, ∞)
USING TECHNOLOGY:
y = - x2
Graphing calculators can aid us on looking at properties of functions:
Vertex: (0,0)
Domain: (- ∞, ∞)
Range: (- ∞, 0)
y=x2 y=4x2
y= -4x2
y= x2
y = - x2
Notice:if coefficient is positive: Parabola faces UP if coefficient is Negative: Parabola faces DOWNif coefficient is > 1: Parabola is Skinnyif coefficient is Between 0 and 1: Parabola is wide
USING TECHNOLOGY: What is the difference and Similarities of :
1) y = 4x2+2 2) y = 4x2-2
3) y = -4x2+2 4) y = -4x2-2
y = 4x2+2
y = 4x2-2
Notice: Y = a(x-h)2 +k
Y = a(x-h) 2 +k
+k shift up
Y = a(x-h) 2 -k
-k shift down
+a faces up
+a faces up
y = -4x2+2
y = -4x2-2
Notice: Y = a(x-h)2 +k
Y = -a (x-h) 2 +k
+k shift up
Y = -a(x-h) 2 -k
-a faces down
-a faces down-k shift down
REAL-WORLD:A person walking across a bridge accidentally drops and orange into the rives below from a height of 40 ft. The function h = -16t2 + 40 gives the orange’s height above the water, in feet, after t seconds. Graph the function. In how many seconds will the orange hit the water?
GRAPHING:t h= -16t2+40 h
0 -16 (0)∙ 2+40 =40 40
-16 (1)∙ 2+40 =24 241
2 -16 (2)∙ 2+40 -24= -24
Notice:We stop after we get a negative height as we Cannot go beyond the ground.
SOLUTION:Once again:
Seconds (t) must start at 0 t = 0
Height (h) must stop at 0 h = 0
Thus: our orange will take about 1.6 seconds to hit
the ground.Seconds (t)
Heig
ht (h
)
VIDEOS: Quadratic Graphs and Their Properties
Interpreting Quadratics:http://www.khanacademy.org/math/algebra/quadratics/quadratic_odds_ends/v/algebra-ii--shifting-quadratic-graphs
http://www.khanacademy.org/math/algebra/quadratics/graphing_quadratics/v/graphing-a-quadratic-function
Graphing Quadratics:
VIDEOS: Quadratic Graphs and Their Properties
Graphing Quadratics:
http://www.khanacademy.org/math/algebra/quadratics/graphing_quadratics/v/quadratic-functions-1
CLASSWORK:
Page 537-539:
Problems: 1, 2, 3, 4, 7, 8, 10, 13, 19, 27, 28, 34 39.