Vertex and Standard Form of Quadratics

Features of Forms

100

What key features does FACTORED FORM tell us?

(list all)

x-intercepts

max/min

200

Identify the key features of the following form:

x² - 11x + 24

y-intercept: 24

minimum vertex

300

Identify the key features of the following form

-(x+2)(x-1)

x intercepts: x=-2     x=1

maximum vertex

400

Identify the form AND the key features

-(x-4)² + 3

vertex form

vertex: (4,3)

maximum

500

Write the quadratic that has the following key features

x-intercepts: x=1   x=-3 ,    minimum vertex

(hint: write it in the form of the given key features!) 

y = (x-1)(x+3)

Converting to Standard Form

100

How do you go from factored form to standard form?

Multiply!!!

200

Convert to standard form

y = (x-1)(x+2)

y = x² + x -2

300

Convert to standard form:

y = (3x+2)(x-4)

y = 3x² - 10x - 8

400

convert to standard form:

y = (x-3)² - 4

y = x² - 6x + 5

500

convert to standard form:

y = 3(x+1)² + 2

y = 3x² + 6x + 5

Converting to Other Forms

100

How do you go from standard form to VERTEX form?

complete the square!

200

Convert to factored form: 

y = x² + 6x + 5

y = (x+1)(x+5)

300

convert to factored form:

y = x² -12x + 35

y = (x-5)(x-7)

400

Convert to Vertex Form:

y = x² - 6x + 5

y = (x-3)² - 4

500

Convert to Vertex form:

y= x² + 12x - 12

What is the vertex?

y = (x+6)² - 48

(-6, -48)

Modeling Quadratics

100

given the expression: -16t²+ v₀t + h₀

what do v₀ and h₀ mean?

v₀ = initial velocity

h₀ = intitial height

200

A ball kicked in the air is modeled by the equation: h(t) = -16t² + 25t + 1.5, where t is the time in seconds and h(t) is the height in feet. 

What is the initial height of the ball? What is the intial velocity of the ball?

intitial height = 1.5 feet

intitial velocity = 25 ft/s

300

A rocket is launched in the air. the equation h(t) = -16t² + 32t + 48 models its path. t is time in seconds, h(t) is feet.

What is the vertex? what do the values mean in context?

(1,64)

after 1 second reaches a max height of 64 feet

400

Ms. Arney threw a water balloon of a building. the equation h(t) = -16t² + 35t + 42 models its path.

What was the maximum height?

When did the balloon hit the ground?

61.14 ft

3.05 seconds

500

Thor is struck off a 102 meter building with an intial velocity of 89 m/s.

Write the equation. find the following.

What is his max height? at what time?

When does Thor land?

 h(t) = -16t² + 89t + 102

225.77 meters at 2.78 seconds

lands after 6.54 seconds