Unit 4 Quadratic Review

​Unit 4 Quadratic Review

By Alexis Hayes

Examples!

Multiple Choice

Question 1

• A

• B

• C

• D

Multiple Choice

Question 2

• A

• B

• C

• D

Multiple Choice

Question 5

• A

• B

• C

• D

Multiple Choice

Question 9

• A

• B

• C

• D

Multiple Choice

Which point represents the y-intercept of the quadratic?

• (-1,0)

• (-2,0)

• (-1.5,-0.25)

• (0,2)

Multiple Choice

What is the domain and range of the parabola?

*There are understood arrows on the ends

• Domain: $$\left(-\infty,\infty\right)$$  

  Range: $$y\ge3$$  

• Domain: $$x\ge3$$  

  Range: $$\left(-\infty,\infty\right)$$  

• Domain: $$\left(-\infty,\infty\right)$$  

  Range: $$y\le3$$  

• Domain: $$\left(-\infty,\infty\right)$$  

  Range: $$\left(-\infty,\infty\right)$$  

• Domain: $$x\le3$$  

  Range: $$\left(-\infty,\infty\right)$$  

Fill in the Blank

What is the maximum value (look at the maximum y coordinate)?

Type the NUMBER only!

Multiple Choice

Where is the function increasing?

• $$\left(-\infty,-1\right)$$

• $$\left(-1,\infty\right)$$

• $$\left(-2,\infty\right)$$

• $$\left(-\infty,-2\right)$$

Multiple Choice

Where is the function decreasing?

• x≤0

• x≥0

• x≤1

• x≥1

Multiple Choice

What is the end behaviors of the graph as $$x\rightarrow\infty$$ and $$x\rightarrow-\infty$$ ?

• The end behavior of the graph is x →∞, y→∞ and x→∞, y→⁻∞

• The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞

• The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞

• The end behavior of the graph is x →∞,y→⁻∞ and x→∞, y→⁻∞

Multiple Choice

Describe the end behavior of the graph as $$x\rightarrow\infty$$ and $$x-\infty$$

• x →∞, y→⁻∞ and x →⁻∞,y→⁻∞
• x →∞, y→∞ and x→⁻∞, y→∞
• x →∞, y→∞ and x→⁻∞, y→0
• x →∞,y→∞ and x→⁻∞, y→⁻∞

Multiple Choice

A ball is launched upward at 20 meters per second (m/s) from a 60 meter tall platform. The equation for the object's height s at time t seconds after launch is s(t) = –4.9t ² + 20t + 60, where s is in meters. What is the greatest height the ball reaches? Round to the nearest hundredth.

• 53.45 m/s

• 67.39 m/s

• 72.34 m/s

• 80.41 m

Multiple Choice

A ball is launched upward at 20 meters per second (m/s) from a 60 meter tall platform. The equation for the object's height s at time t seconds after launch is s(t) = –4.9t ² + 20t + 60, where s is in meters. How long is the ball in the air? Round to the nearest hundredth.

• 6.09 secs

• 3.50 secs

• 4.72 secs

• 1.25 secs

Multiple Choice

A ball is launched upward at 20 meters per second (m/s) from a 60 meter tall platform. The equation for the object's height s at time t seconds after launch is s(t) = –4.9t ² + 20t + 60, where s is in meters. How high is the ball at 3 secs ? Round to the nearest tenth.

• 56.7 m/s

• 34.2 m/s

• 75.9 m/s

• 80.1 m/s

Multiple Choice

A ball is launched upward at 20 meters per second (m/s) from a 60 meter tall platform. The equation for the object's height s at time t seconds after launch is s(t) = –4.9t ² + 20t + 60, where s is in meters. How high is the ball at 6 seconds?

• 1.5 m/s

• 3.6 m/s

• 2.4 m/s

• 5.5 m/s

Multiple Choice

A book was dropped from the top of a building. If the book reaches the ground in 4 seconds, which function models the height in feet of the book after t seconds?

• h(t)= -16t²

• h(t)-16t²+4

• h(t)=-16t²+16

• h(t)=-16t²+256

Multiple Choice

Write the equation for a transformed version of

f(x)=x²

that meets the following criteria

(1) Reflects across the x-axis.

(2) Shifts 3 units to the left and 2 units up.

• $$f\left(x\right)=-\left(x-3\right)^2-2$$

• $$f\left(x\right)=-\left(x+3\right)^2+2$$

• $$f\left(x\right)=\left(x^2+3\right)-2$$

• $$f\left(x\right)=\left(x-3\right)^2+2$$

Multiple Choice

Write the equation for a transformed version of

y=x²

shift 1 unit to the right and 5 units down

• y=(x-1)²-5

• y=(x+1)²+5

• y=(x-1)²+5

• y=(x+1)²-5

Multiple Choice

What is the transformation of the graph?

• f(x)=(x-5)²-9

• f(x)=(x-9)²-5

• f(x)=(x-9)²+5

• f(x)=(x+5)²+9

​Average Rate of Change

Multiple Choice

What is the average rate of change of the function $$f\left(x\right)=-2x^2+3x-5\$$ on the interval $$0\le x\le2$$ ?

• -4

• -2

• -1

• 1

​Area Model- Multiply Binomial

Multiple Choice

The length of a square is x + 2 units.  Find the area.

• 4x + 8 units squared
• x² + 4x + 4 units squared
• x² + 4 units squared
• Not enough information

Multiple Choice

The length of a rectangle is x + 2 units and the width is 3x + 7
 units. Find the area.

• 3x² + 9x + 14 square units
• 3x² + 13x + 14 square units
• 4x + 9 square units
• 8x + 18 square units

Multiple Choice

Find the area of a rectangle with length (x - 5) and width (3x + 1).

• 3x²+16x-5
• 3x²-14x+5
• 3x²-14x-5

Multiple Choice

A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters.

What will be the width of the pathway?

• x=4

• x = 2.3

• x=1.5

• x=3

​Comparing Quadratic Functions

Multiple Choice

The graph of  $$f\left(x\right)=x^2$$  is shown on the grid.
Which statement about the relationship between the graph of  $$f$$  and the graph of $$g\left(x\right)=7x^2$$   is true?

• The graph of  $$g$$   is narrower than the graph of $$f$$  .

• The graph of $$g$$   is wider than the graph of $$f$$  .

• The graph of  $$g\$$ is 7 units below the graph of $$f$$  .

• The graph of $$g$$  is 7 units above the graph of $$f$$  .

Multiple Choice

Compare ƒ(x) = -2x² - 8x + 20 to the graph of g(x) shown.  What can you conclude about the two functions?

•  ƒ(x) has a greater maximum than g(x).

• g(x) has a greater maximum than ƒ(x).

• ƒ(x) has a minimum, while g(x) has a maximum.

• g(x) and ƒ(x) have the same maximum.

Multiple Select

The equation f(x)= - (x+7)² +3 represents f(x), and the graph represents g(x). Select all of the true statements about the two functions

• The line of symmetry of g(x) is x=1

• The maximum of g(x) is less than the maximum of f(x)

• The value of x when f(x) is at its maximum is less than the value of x when g(x) is at its maximum

• g(x) has a vertex value that is a minimum

• f(x)'s graph is a parabola opening down

Multiple Choice

Compare g(x) to f(x). Which statement is true?

• g(x) has 2 negative x-intercepts.

• f(x) has one positive and one negative x-intercepts.

• f(x) has 2 positive x-intercepts.

• g(x) has 2 positive x-intercepts.