Algebra II Honors Notes
Dec 10, 2012
Name _________________
EXPLORING QUADRATIC FUNCTIONS on the TI-83+
A quadratic function is any function in the form y  ax  bx c or y  a(x  h)  k .
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All quadratic functions graph into ________________________.
You will be exploring quadratic functions on your own, making conjectures about the effect of changing various parts of the
formula, which of the “letters” in the formula has changed, and its effect on the graph. For each variation from “normal”,
graph the following functions on your graphing calculator. Your window should be the standard window (Zoom 6) x-min 10, x-max 10, y-min -10, and y-max 10.
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Look at the standard form y  a(x  h)  k and figure out which variables (a, h, or k) are
being changed and which variables (a, h, or k) are being held constant. Hint: Imagine rewriting
y  x as y  1x  0  0 and y  x  2 as y  1x  0  2 .
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Use the lines below to describe each graph: Use words such as “normal” size, [“normal” being the size of y  x ] , wider
or more narrow than normal, “vertex at origin,” “moves up 4,” “moves left 3,” “turns up” or “turns down”, etc.
Section A:
Which variable changed? (Choose from a, h, or k) ____
1. y  x
2
_____________________________________________
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2. y  x  2
_____________________________________________
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3. y  x  5
_____________________________________________
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4. y  x  1
_____________________________________________
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5. y  x  7
_____________________________________________
Clear the graphs from Section A. Then graph the following functions:
Section B:
Which variable changed? (Choose from a, h, or k) ____
1. y  x
2
_____________________________________________
2. y  x  2
_____________________________________________
3. y  x  6
_____________________________________________
4. y  x  4
_____________________________________________
5. y  x  8
_____________________________________________
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EXPLORING QUADRATIC FUNCTIONS
y  a(x  h)2  k.
Clear the graphs from Section B. Then graph the following functions:
Which variable changed? (Choose from a, h, or k) ____
Section C:
1. y  x
2
2. y  3x
3.
y
_____________________________________________
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2 2
x
3
4. y  7x
5.
y
_____________________________________________
_____________________________________________
2
_____________________________________________
1 2
x
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6. y   x
_____________________________________________
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7. y  0.3x
_____________________________________________
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_____________________________________________
Make TWO observations about the effect that a has on the graph:
In summary:
a affects ___________________________________________________
h affects _____________________________________________________
k affects _____________________________________________________
A.52 - Algebra II Honors
Due Wed, Dec 7
Name _________________
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y  a(x  h)  k
Use the four conjectures that you have written to predict the appearance of the following parabolas.
When making comments, choose one from each of the following groups:
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SIZE - normal size, narrower than normal, or wider than normal (normal being the size of y  x )
HORIZONTAL SHIFT - no horizontal movement, moves right _?_ units, moves left _?_ units
VERTICAL SHIFT - no vertical movement, moves up _?_ units, moves down _?_ units
ORIENTATION - turns up or turns down
Feel free to check your answers using the graphing calculator.
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#1. y  x  4
#2. y  x  3
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#3. y  x  5 1
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#4. y  x  2  3
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#5. y  3x  2   4
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y   x  1
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#6.
#7. y   x  2  3
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#8. y  100x  12
#9. Write a quadratic function of a parabola the is wider than normal, three units left, five units
up, and turns down.
#10. Make up your own problem. Write it here and check your answer on the GC. Then write
your answer upside down at the bottom of this page.