Transcript (Ch. 2) Test Review Slideshow

Section 2.2 Review
AND CHAPTER 2 TEST REVIEW
Parent Graphs/General Equations of 8 Families of Functions:
y  a  x  h  k
yx
Linear
Exponential Growth (b>1)
y  ab x h  k
y  ab x
Exponential Decay (0<b<1)
x h
x
Quadratic
Square Root
Cubic
Absolute Value
Reciprocal or Hyperbola
y  ab
y  ab
yx
y  a  x  h  k
2
k
2
y x
y a x h k
y  x3
y  a  x  h  k
y x
y a x h k
1
y
x
a
y
k
x h
3
Even/Odd Functions (Reflections)
Even Functions:
◦ If f(-x) = f(x), the function is even.
◦ The graph of f(x) will be SYMMETRIC ABOUT THE Y-AXIS.
Odd Functions:
◦ If f(-x) = -f(x), the function is odd.
◦ The graph of f(x) will have 180o ROTATIONAL SYMMETRY.
Therefore, the transformation to reflect across the y-axis is to multiply the input (x) by -1 {f(-x)}
As previously learned, the transformation to reflect across the x-axis is to multiply the entire
function by -1 {-f(x)}
Write the equation for these graphs.
(2, 3)
(0, -17/4)
(-2, -5)
(1, -4)
ANSWERS:
1
y  ( x  1)3  4
4
y  4 x  2 5
Sketch the graphs of the functions.
y  2( x  3) 2  3
y  3 x  6  1
ANSWERS:
Points on
Graph:
(-3, 3)
(-2, 1)
(-4, 1)
(-5, -5)
(-1, -5)
Points on
Graph:
(-6, -1)
(-5, -4)
(-2, -7)
(3, -10)
Sketch the graph and write the equation (in
graphing form) for the following descriptions.
1.
An absolute value function with a vertex of (-1, 2) and negative orientation.
2.
A reciprocal function shifted down 2 units and shifted to the left 4 units.
3.
A cubic function with a locator point of (4, 3) and compressed by a factor of ½.
ANSWERS:
y   x 1  2
1
y
2
x4
1
y  ( x  4)3  3
2
Other Topics We Covered (old slideshow)
Quadratic Transformations
◦
◦
◦
◦
◦
Stretch/Compress
Shift Left and Right
Shift Up and Down
Flip Up and Down
Finding the Vertex
Graphing Form vs. Standard Form
Modeling with Parabolas
Distance Between 2 Points (CP)
Writing Equation of a Line Given 2 Points (CP)
Factoring
Simplifying Radicals
◦ Prime Factorization
◦ Completing the Square
◦ Averaging the Intercepts
Sketching a Parabola from Graphing Form
◦ Over 1 and 2, Up 1 and 4 (Stretch Factor??)
**REMINDER: NO CALCULATOR!!!!
Simplifying Radicals
Use prime factorization to break the value down into its prime factors.
Find a matching group of items equal to the index of the radical and
bring that item to the front.
Anything left will remain under the radical.
Combine ”like” radicals if necessary.
Examples
45  80  5
384x100 y 5
98x3 y 6
4 x33 y 3 6 xy 2
7 xy 3 2 x
3
ANSWERS:
8 5
Modeling Parabolas
Sketch the graph according to the information presented in the problem.
Use the given information to determine your vertex.
Use the vertex and any other point on the graph to find the value of “a”.
Write the graphing form of the equation with your values of “a”, “h”, and “k”.
Example
In a neighborhood water balloon battle, Benjamin has his home base
situated 20 feet behind a 30 foot-high fence. Twenty feet away on
the other side of the fence is his enemy’s camp. Benjamin uses a
water balloon launcher ands shoots his balloons so that they just
miss the fence and land in his opponent’s camp. Write an equation
that, when graphed, will model the trajectory of the water balloon?
ANSWER: y = -3/40(x – 20)2 + 30
Factoring
First, factor out any common value with each term (greatest
common factor - GCF).
Use “box and diamond” method to factor your trinomial (3 terms)
into the product of two binomials (2 terms each).
◦ Add a 0x term if necessary.
Only SOLVE FOR X if the trinomial was originally set equal to 0.
Otherwise, you are just rewriting the trinomial in factored form.
Examples
x2  8x  9
9 x5  21x 2
x 2  144
ANSWERS:
( x  9)( x  1)
3 x 2 (3 x3  7)
( x  12)( x  12)