Unit 4 Part 1 Review

Quadratic Characteristics

100

What is the vertex of the graph: f(x)=x^2-2x+3?

(1,2)

200

What is the axis of symmetry of the graph: f(x)=x^2-2x+3?

x=1

300

What is the domain of the graph: f(x)=x^2-2x+3?

(-∞,∞)

400

What is the range of the graph: f(x)=x^2-2x+3

[2,∞) 

500

What is the end behavior of the graph: f(x)=x^2-2x+3

x-->∞ f(x)-->

x-->-∞ f(x)-->

∞ 

∞

Contextual Problems

100

The Demon Drop at Cedar Point in Ohio takes riders to the top of a tower and drops them 60 feet. A function that approximates this ride is h(t)= -16t^2 + 64t + 60, where h is the height in feet and t is the time in seconds. What is the initial height of the ride?

y-intercept (0,60)

60 feet

200

The Demon Drop at Cedar Point in Ohio takes riders to the top of a tower and drops them 60 feet. A function that approximates this ride is h(t)= -16t^2 + 64t + 60, where h is the height in feet and t is the time in seconds. What are the x-intercepts? Which one can be ignored and why?

(-0.784,0) & (4.784,0)

(-0.784,0), negative time doesn't exist

300

The Demon Drop at Cedar Point in Ohio takes riders to the top of a tower and drops them 60 feet. A function that approximates this ride is h(t)=-16t^2 + 64t + 60, where h is the height in feet and t is the time in seconds. When does the ride end (or drop to the ground)?

4.784 seconds (x-intercept)

400

The Demon Drop at Cedar Point in Ohio takes riders to the top of a tower and drops them 60 feet. A function that approximates this ride is h(t)=-16t^2 + 64t + 60, where h is the height in feet and t is the time in seconds. What is the vertex of the graph? What does it mean in the context of this problem?

(2,124)

In 2 seconds, the ride reaches a maximum height of 124 ft. 

500

The Demon Drop at Cedar Point in Ohio takes riders to the top of a tower and drops them 60 feet. A function that approximates this ride is h(t)=-16t^2 + 64t + 60, where h is the height in feet and t is the time in seconds. What is the domain of this problem? What does it mean in context?

Domain: [0,4.784]

Total time the ride takes

Transformations

100

Describe the transformations of the graph from the parent graph x^2: f(x)=x^2 +2

Moves 2 units up

200

Describe the transformations of the graph from the parent graph x^2: f(x)=(x-4)^2

Moves 4 units to the right

300

Describe the transformations of the graph from the parent graph x^2: f(x)=(x+3)^2

Moves 3 units to the left

400

Describe the transformations of the graph from the parent graph x^2: f(x)=3(x+2)^2+5

-vertical stretch by a factor of 3

-moves 2 units left

-moves 5 units up

500

Write the equation of the quadratic that has undergone these transformations:

-reflect over the x-axis

-moves right 4 units

-moves down 2 units

f(x)=-(x-4)^2-2

Converting to Standard Form

100

Convert: y=(x-3)(x+4)

y=x^2+x-12

200

Convert: y=(x-5)(x-5)

y=x^2-25

300

Convert: y=(x+2)^2

y=x^2+4x+4

400

Convert: y=(x+4)^2-6

y=x^2+8x+10

500

Convert: y=2(x+3)^2-5

y=2x^2+12x+13

Vocabulary

100

What is the turning point of a quadratic graph called?

The vertex

200

If the vertex is the top point of the graph, what is it called?

Maximum

300

If the vertex is the bottom point of the graph, what is it called?

Minimum

400

What does end behavior mean?

What happens at the end of the graph, the direction of f(x) or y-values, etc.

500

What are the values that cross the x-axis of a quadratic function called? (3 names)

x-intercepts, zeros, roots