Section 2.2 ReviewAND CHAPTER 2 TEST REVIEW

Parent Graphs/General Equations of 8 Families of Functions:

Linear

Exponential Growth (b>1)

Exponential Decay (0<b<1)

Quadratic

Square Root

Cubic

Absolute Value

Reciprocal or Hyperbola

2

3

x h

x h

y a x h k

y ab k

y ab k

y a x h k

y a x h k

y a x h k

y a x h k

ay k

x h

2

3

1

x

x

y x

y ab

y ab

y x

y x

y x

y x

yx

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.

(1, -4)

(0, -17/4)

31( 1) 44

y x

(-2, -5)

(2, 3)

4 2 5y x ANSWERS:

Sketch the graphs of the functions.

22( 3) 3y x 3 6 1y x

Points on Graph:(-3, 3)(-2, 1)(-4, 1)(-5, -5)(-1, -5)

Points on Graph:(-6, -1)(-5, -4)(-2, -7)(3, -10)

ANSWERS:

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.

1 2y x 12

4y

x

31

( 4) 32

y x ANSWERS:

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◦ Completing the Square◦ Averaging the Intercepts

Sketching a Parabola from Graphing Form◦ Over 1 and 2, Up 1 and 4 (Stretch Factor??)

Modeling with Parabolas

Distance Between 2 Points (CP)

Writing Equation of a Line Given 2 Points (CP)

Factoring

Simplifying Radicals◦ Prime Factorization

**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

ANSWERS:

45 80 5 100 53 384x y 3 698x y

8 5 33 234 6x y xy 37 2xy x

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

ANSWERS:

2 8 9x x

( 9)( 1)x x

5 29 21x x

2 33 (3 7)x x

2 144x

( 12)( 12)x x

I can statements . . .

Are you prepared?

I can write an equation of a transformed parent function from a description.I can write an equation of a transformed parent function from a graph.I can write a quadratic equation to model a real world situation such as throwing a ball.

I can find the x and y intercepts of a quadratic function.I can simplify exponential expressions.I can simplify radical expressions.I can sketch the graph of a transformed parent function given the equation in graphing form.

I can write the equation of a line in point-slope form given two points.I can put a quadratic function in graphing form by completing the square or averaging the intercepts and then name the coordinates of the vertex.

I can identify exponential growth and exponential decay equations.