Linear and Quadratic Review

Linear and Quadratic Review

Let's review....

Is it Linear or Quadratic? 2x+5y=20

• What is the highest exponent?

• If it is x¹= linear

• If it is an x² =quadratic

Multiple Choice

Is it linear, quadratic, or exponential?

• Linear

• Quadratic

• Exponential

• Outrageously outrageous

Multiple Choice

Is it linear, quadratic, or exponential?

• Linear

• Quadratic

• Exponential

• Outrageously outrageous

Multiple Choice

3x² - 12 = 0

• Linear Equation

• Quadratic Equation

• Neither

Multiple Choice

2x – 5 = 0

• Linear Equation

• Quadratic Equation

• Neither

Multiple Select

x² – 4x + 7 = 0

• Linear Equation

• Quadratic Equation

• Neither

Let's look at linear equations and their characteristics

Slope

There are 4 types of slope with Linear Equations

• Positive

• Negative

• Zero (horizontal)

• Undefined ( vertical)

Multiple Choice

What is the slope?

• Positive
• Negative
• Zero
• Undefined

Multiple Choice

What is the slope?

• Positive
• Negative
• Zero
• No Slope

Multiple Choice

Identify the type of slope.

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Identify the type of slope.

• Postive

• Negative

• Zero

• Undefined

Multiple Choice

What is the slope of all horizontal lines?

• 0
• undefined
• 1
• -1

Multiple Choice

What direction is an undefined slope?

• horizontal
• vertical

Multiple Choice

Find the slope.

• m = 0

• m = 6

• Undefined

• No solution

Multiple Choice

What direction is a line with an undefined slope?

• horizontal
• vertical
• increasing
• decreasing

There is more to slope though...

• Slope is rise/run

• Slope tells us how we move from one point to another.

• But we can't forget the positive or negative part.

• We need slope to help us come up with the equation of a line.

• There are several ways to find slope.

Slope from a picture....show me

• First we need to find two "perfect points"

• Let's use (0,-2) and (-3,-1)

• 
  

• 
  

• 
  

Calculate the slope

• Count the rise 1

• Count the run 3

• Is it positive or negative -

• Set up fraction= +/- rise/run= -1/3

• There's your slope.

Multiple Choice

Find the slope

• -5/3
• -3/5
• 5/3
• 3/5

Multiple Choice

Find the slope

• -5/3
• -3/5
• 5/3
• 3/5

Multiple Choice

Find the slope of the line.

• -5/4
• 5/4
• -4/5
• 4/5

Multiple Choice

Find the slope:

• 3/4
• 4/3
• -3/4
• -4/3

Multiple Choice

Find the slope:

• 2
• -2
• 1/2
• -1/2

Another way to find slope

• Sometimes you are given two points and asked to find the slope.

• Step 1: Plot the points on Desmos

• Count the rise

• Count the run

• Is it positive or negative?

• Set up the fraction +/- rise/run

• Make sure it's reduced! (use Desmos)

Multiple Choice

Find the slope given these points:

(2,-4) & (3,1)

• 5

• -3

• 3

• -5

Multiple Choice

Find the slope given these points:

(-5,3) & (3,5)

• 1/4

• 4

• 1

• -1

Multiple Choice

Find the slope given these points:

(1,2) & (3,4)

• 1

• 2

• -1

• -2

Multiple Choice

Find the slope given these points:

(-2,-3) & (2,3)

• 3/2

• 0

• undefined

• -3/2

Quadratics have "slope" too

• It's not slope like with lines though

• It is simply either positive - opening up

• or negative - opening down

• This can be important in identifying what graph or equation we should look at.

• 
  

• 
  

• 
  

Multiple Choice

What direction is the following equation opening?
y=-3x²-7x+8

• Up
• Down
• Left
• Right

Fill in the Blanks

What direction is the following equation opening?

 $y=-2x^2-3x+4$  

Fill in the Blanks

What direction is the following equation opening?

 $x^2-5x+2$  

Fill in the Blanks

What direction is the following equation opening?

 $-x^2+5x-8$