Unit 4B Review

​Unit 4B Review & Study

By Aidan Bullard

Purpose of the Unit

• Define Characteristics of Quadratics from a Graph/Equation

• Convert Quadratics from Standard to Vertex Form

• Define and Apply Transformations to a Quadratic Function

Quadratic Forms

Multiple Choice

What is the y-intercept for the function:

$$-x^2+2x+5$$

• (0,5)

• (5,0)

• 5

• (0,-5)

Multiple Choice

What is the x-intercepts for the function:

2(x-2)(x+3)

• (-3,0)

• (-2,0)

• (2,0)

• (3,0)

Multiple Choice

What is the vertex for the function:

$$\left(x+9\right)^2-3$$

• (9,-3)

• (-9,-3)

• (-9,-3)

• (9,3)

Characteristics from a Quadratic Graph

Domain: All possible x-values
Range: All possibly y-values
Vertex: Maximum/Minimum/Transition point between increasing and decreasing
Axis of Symmetry: Line that can cut a quadratic perfectly in half (Found at the vertex)

x-intercepts: Point where the line intercepts the x-axis
y-intercept: Point where the line intercepts the y-axis
Interval of Increase: Domain(x-values) where the line is increasing
Interval of Decrease: Domain where the line is decreasing

Multiple Choice

What is the axis of Symmetry?

• y=-4

• x=-4

• x=0

• y=0

Multiple Choice

What is the Vertex?

• (0,-3)

• (0,0)

• (-4,0)

• (0,-4)

Multiple Select

What are the x-intercepts?

• (-2,0)

• (2,0)

• (0,-4)

• No solution

Multiple Select

What are the Domain and Range?

• D:[-4,4]

• R:[-4,4]

• D: (∞,-∞)

• R:[-4,∞)

Multiple Select

What is the interval of Increase and Decrease?

• Increasing: (0,∞)

• Decreasing:[-4,0)

• Increasing:[0,∞)

• Decreasing:(-∞,0)

Multiple Choice

What is the Y-intercept?

• (-2,0)

• (0,-4)

• (-4,0)

• (2,0)

Completing the Square

Purpose: Converting from Standard form to Vertex Form
- Allows for you to get more information on the function characteristics even when given just the standard or factor form

Open Ended

Use Completing the Square to find the Vertex form:

$$x^2+2x+3$$

Open Ended

Use Completing the Square to find the Vertex Form:

$$x^2+4x-9$$

Transformations of Quadratic Functions

Multiple Choice

What steps transform the graph y = x² to y = 2(x+2)² - 5?

• Compress by 2, shifted 2 units left and 5 down

• Stretch by 5, shifted 5 units left and 2 down

• Stretch by 2, shifted 2 units left and 5 down

• Compress by 5, shifted 2 units left and 2 down

Multiple Choice

What steps transform the graph y = x² to y = x² + 8

• shifted up 8 units

• shifted down 8 units

• shifted left 8 units

• shifted right 8 units

Multiple Choice

What steps transform the graph y = x² to y = (x-4)²

• Shifted down 4 units

• Shifted left 4 units

• Shifted right 4 units

• Shifted up 4 units

Multiple Choice

Compare the function y = 0.3x² to the parent function y = x²

• Wider
• Narrower

Average Rate of Change

Multiple Choice

What is Mrs. Gordon's rate from 0 to 2 seconds?

• 2.5 feet per second
• .4 feet per second
• 5 feet per second
• .2 feet per second

Multiple Choice

Calculate the average rate of change from 20 to 40 minutes.

• -2 minutes per gallon

• -20 minutes per gallon

• -2 gallons per minute

• -20 gallons per minute

Multiple Choice

What is the average rate of change from x=0 to x=1

• -3
• 3
• 0
• 2

Multiple Choice

Which of the following intervals has the largest average rate of change?

• [13,14]
• [13, 17]
• [16, 17]
• [16, 19]

Similar Test Questions

Multiple Select

$$-x^2+4x+7$$ :

Choose 3 statements that appropriately describe the quadratic

• The graph opens down

• The y-intercept is (0,7)

• The vertex is (3,11)

• The axis of symmetry is at x=2

Multiple Select

$$-3x^2+27x$$ :

Choose the options representing an x-intercept and the maximum of the quadratic

• x-intercept: (0,9)

• x-intercept: (9,0)

• Maximum: (4.5,60.75)

• Maximum: (-4.5,-60.75)

Multiple Choice

Which answer choice best represents the domain and range of the function?

• Domain: x ≥ −3 Range: y ≥ 5

• Domain: All real numbers

  Range: y ≥ 5

• Domain: x ≥ −3 Range: All real numbers

• Domain: y ≥ 5 Range: x ≥ −3

Multiple Choice

Function h can be used to model the height in feet of a rocket from the ground t seconds after it was launched. What was the range of its trajectory?

• 0 < y < 225

• 0 < x < 7.5

• 0 ≤ y ≤ 225

• 0 ≤ x ≤ 7.5

Multiple Choice

A golfer hit a golf ball from a tee box that is 6 yards above the ground. The graph shows the height in yards of the golf ball above the ground as a quadratic function of x, the horizontal distance in yards of the golf ball from the tee box. What is the domain of the function for this situation?

• 0 ≤ x ≤ 230

• 6 ≤ y ≤ 36

• 0 ≤ y ≤ 36

• 6 ≤ x ≤ 230

Multiple Select

The trajectory of a basketball is modeled by the function:

f(x)= $$-x^2+5x+1$$ , where f(x) is the height of the basketball after x seconds. What is the domain and range of the function?

• Domain:

  (-∞,∞)

• Range:

  [0,7.25]

• Domain:

  [0,5.19]

• Range:

  (-∞,7.25]

Multiple Choice

$$x^2+8x+24$$

What is true about the two functions presented?

• They are both linear

• The table is linear and the equation is quadratic

• The equation is linear and the table is quadratic

• They are both quadratic

Multiple Choice

$$h\left(x\right)=2x^2+4x+10$$

If I apply the transformation h(x-4), how does h(x) move?

• Up by 4 units

• Right by 4 units

• Left by 4 units

• Down by 4 units

Multiple Choice

A baseball is hit into the air with a trajectory of $$f\left(x\right)=-x^2+7x$$ . Johnny wants to know the height of the baseball after 2 and 4 seconds. Which option is TRUE based on the values of f(2) and f(4)

• f(2) = 9

• f(2) = 11

• f(4) = 12

• f(4) = 11

Multiple Choice

You are given the function: $$f\left(x\right)=x+2$$ and the parabola provided. Which interval are BOTH functions Increasing?

• (-∞,∞)

• (-∞,-2)

• (-2,∞)

• (-2,2)

Multiple Choice

What is the average rate of change between x=-1 and x=2?

• 3

• Undefined

• 1

• -1

Multiple Choice

What is Mrs. Gordon's rate from 0 to 2 seconds?

• 2.5 feet per second
• .4 feet per second
• 5 feet per second
• .2 feet per second

Multiple Choice

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

• 2
• 1/2
• -2
• -1/2

Multiple Choice

Which transformation transforms the graph of

f(x) = x² to the graph of g(x) = (x + 4)²?

• shift 4 units up

• shift 4 units down

• shift 4 units to the left

• shift 4 units to the right

Multiple Choice

If the blue graph is
f(x) = x² 
then the red must be...

• g(x) = x² - 5
• g(x) = x² + 5
• g(x) = (x - 5)²
• g(x) = (x + 5)²