Algebra II - Are you Ready?

Algebra II - Are you Ready?

Part I is over - now it's time for part 2

Linear Functions

This year we talked about Linear Functions and other functions that came from them.

Linear Absolute Value Functions

Linear absolute value functions are one of the functions we learned about from linear functions.

Exponential Functions

Aside from lines, we talked about a curvy function known as the exponential function.

Quadratic Functions

The next place to go is our other curvy friends: Quadratic Functions....

Going Back to Go Forward

Lets review some key information.....

Key Structures:

• y-intercept: where the graph crosses the y-axis

• x-intercept: where the graph crosses the x-axis

Multiple Choice

Where is the y-intercept in this graph?

• (0,2)

• (4,0)

Multiple Choice

Where is the x-intercept in this graph?

• (0,2)

• (4,0)

Key Features: Absolute Value

• Vertex (corner point): where the graph turns from decreasing to increasing

• Axis of Symmetry: an invisible line that cuts the graph into two equal halves through the vertex

Multiple Choice

Where is the vertex of this graph?

• (0,3)

• (3,0)

Multiple Choice

Where is the axis of symmetry of this graph?

• x = 3

• x = 0

Open Ended

Compare the linear function to the Quadratic - what do you notice about the x-intercepts?

Open Ended

Compare the Linear Absolute Value Function to the Quadratic Function. What key feature(s) do they share?

Quadratics are the same!

Quadratics have all of these key structures too!

3 forms of Functions

Linear functions have 3 different forms, each that give different advantages.

Multiple Choice

Which form of line is this?

• Point-Slope Form

• Slope-Intercept Form

• Standard Form

Multiple Choice

Which form of line is this?

• Point-Slope Form

• Slope-Intercept Form

• Standard Form

Multiple Choice

Which form of line is this?

• Point-Slope Form

• Slope-Intercept Form

• Standard Form

Quadratics are the same!

Quadratics also have 3 forms of functions that have different uses!

The Golden Rule of Algebra

Remember, solving doesn't go away!

X-intercepts AKA "Zeros"

Quadratics have a special structure called "Zeros". They are called this because they are where the quadratic equals 0!

Fill in the Blanks

Solve this equation for x:  $x-2=0$  

Fill in the Blanks

Solve this equation for x:  $x+5=0$  

Fill in the Blanks

Solve this equation for x:  $3x-6=0$  

Easy Right?

Well, it will get more challenging from there...but if you know the key structures, the rest will follow!