84 transforming quadratic functions
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Alg1 Notes 8.4.notebook March 28, 2013
84 Transforming Quadratic Functions
1. Right this very moment, do the 8.18.4 Practice Quiz worksheet. Questions 5 8 are on today's lesson so show me what you know, it is OK if you don't know these.
2. Once you are done, raise your hand and I will check your homework.
84 Transforming Quadratic Functions
Graph and Transform quadratic functions
You can compare how long it takes raindrops to reach the ground from different heights.
Alg1 Notes 8.4.notebook March 28, 2013
The parent graph: y = x2
Note, we now know two parent graphs:A line: y = x and a parabola: y = x2
I. Shifts Up and Down: A Line
y = x y = x + 4 y = x 3–
Alg1 Notes 8.4.notebook March 28, 2013
I. Shifts Up and Down: A Parabola
y = x2 3–y = x2 + 4y = x2
1. Identify the shift, then sketch
y = x2 + 2 y = x2 5–
How could you check?
Alg1 Notes 8.4.notebook March 28, 2013
II. Steepness of a Line
y = x y = 2x
II. Steepness (Width) of a Parabola
y = 2x2 y = x2
Alg1 Notes 8.4.notebook March 28, 2013
III. Flips over the xaxis
y = 2x2 y = x2
2. Order the functions from narrowest graph to widest.
a. f(x) = 3x2, g(x) = 0.5x2 The function with the narrowest graph has the greatest |a|.
Check Use a graphing calculator to compare the graphs
b. f(x) = x2, g(x) = 1/2x2, h(x) = 2x2
c. ,
d. , ,
Alg1 Notes 8.4.notebook March 28, 2013
IV. All Together Now
Compare the graph of the function with the parent graph: f(x) = x2.
Comment on width, direction, axis of symmetry, translation and vertex.
3.
Width: The graph of g(x) is wider than f(x).Direction: The graph of g(x) opens downward and
f(x) opens upward.Axis of Symmetry: The axis of symmetry is the same.
Vertex/Translated? The vertex of g(x) is translated 3 units up to (0, 3)
Sketch four parabola graphs*see if you can come up with their equation.
1) The parent graph2) Wider than the parent graph3) Narrower than the parent graph4) Downward parent graph
Just for Fun...
Alg1 Notes 8.4.notebook March 28, 2013
Compare the graph of the function with the parent graph: f(x) = x2.
Comment on width, direction, axis of symmetry, translation and vertex.
4. g(x) = 3x2
5. g(x) = –x2 – 4
Compare the graph of the function with the parent graph: f(x) = x2.
Comment on width, direction, axis of symmetry, translation and vertex.
Alg1 Notes 8.4.notebook March 28, 2013
6. g(x) = 3x2 + 9
Compare the graph of the function with the parent graph: f(x) = x2.
Comment on width, direction, axis of symmetry, translation and vertex.
Compare the graph of the function with the parent graph: f(x) = x2.
Comment on width, direction, axis of symmetry, translation and vertex.
7.
Alg1 Notes 8.4.notebook March 28, 2013
V. Application
The quadratic function h(t) = –16t2 + c can be used to approximate the height h in feet above the ground of a falling object t seconds after it is dropped from a height of c feet.
Use a graphing calculator. Since time and height cannot be negative, set the window for nonnegative values.
The water balloon dropped from 64 ft reaches the ground in 2 seconds. The ball dropped from 144 feet reaches the ground in 3 seconds.
Right now, go back to your practice quiz and let's see if you can answer #5 8.
Give quiz now!