Quadratics & Polynomials Test Review

Quadratic Applications

Multiple Choice

Which one are we looking for?

Jaiden wanted to know the initial height of a baseball when it was hit at home plate.

• x at vertex

• y at vertex

• x-intercept

• y-intercept

Multiple Choice

Which one are we looking for?

Darrell is trying to find out how many seconds it will take a golf ball to get to its highest point after being hit on the golf course.

• x at vertex

• y at vertex

• x-intercept

• y-intercept

Multiple Choice

Which one are we looking for?

Elliot wants to know how high the soccer ball will get if he kicks it straight up in the air.

• x at vertex

• y at vertex

• x-intercept

• y-intercept

Multiple Choice

Which one are we looking for?

Isabella wants to know how long her toy rocket will be in the air after she lights the fuse to launch it from a 1.5-foot launch pad.

• x at vertex

• y at vertex

• x-intercept

• y-intercept

Multiple Choice

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

• 4 seconds

• -2 seconds

• 6 seconds

• 9 seconds

Multiple Choice

What is the Domain?

• [0, 4]

• [4, 7]

• [0, 7]

• [0, 6]

Multiple Choice

What is the Range?

• [0, 4]

• [4, 7]

• [0, 3]

• [0, 6.8]

Multiple Choice

What was the initial height of the ball?

• 6.8 feet

• 4 feet

• 0 feet

Multiple Choice

How high is the ball at 1 seconds?

• 6 feet

• 4 feet

• 6.8 feet

• 0 feet

Quadratic & Polynomial Key Characteristics and Sketching

Including... Domain, Range, Vertex, Axis of Symmetry, End Behavior, X & Y Intercepts, Factored Form, Max & Min, and Intervals of Increase and Decrease.

Multiple Choice

What is the vertex of this parabola?

• (−1, 3)
• (−3, 11)
• (−2, 5)
• (0, 5)

Multiple Choice

What is the y-intercept of this parabola?

• (−1, 3)
• (−3, 11)
• (−2, 5)
• (0, 5)

Multiple Choice

What is the equation of the parabola?

• $$y=\left(x+1\right)\left(x+3\right)$$  

• $$y=\left(x-1\right)\left(x+3\right)$$  

• $$y=\left(x+1\right)\left(x-3\right)$$  

• $$y=\left(x-1\right)\left(x-3\right)$$  

Multiple Choice

What is the equation of the parabola?

• $$y=\left(x-2\right)\left(x+4\right)$$  

• $$y=\left(x-2\right)\left(x-4\right)$$  

• $$y=\left(x+2\right)\left(x+4\right)$$  

• $$y=\left(x+2\right)\left(x-4\right)$$  

Multiple Choice

What is the vertex?

• (-1,8)

• (8,-1)

• (0,6)

• (-2,6)

Multiple Choice

What is the domain and range of the quadratic function?

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

  Range: $$\left[-7,\infty\right)$$   

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

  Range: $$\left(-\infty,-7\right]$$   

• Domain: $$\left[-7,\infty\right)$$  

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

• Domain: $$\left(-\infty,-7\right]$$  

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

Multiple Choice

Which quadratic equation models the parabola shown?

• y = (x-2)(x+5)

• y = (x+2)(x+5)

• y = -(x-2)(x-5)

• y = -(x+2)(x+5)

Multiple Choice

What is the equation of the parabola?

• $$y=\left(x-2\right)\left(x+4\right)$$  

• $$y=\left(x-2\right)\left(x-4\right)$$  

• $$y=\left(x+2\right)\left(x+4\right)$$  

• $$y=\left(x+2\right)\left(x-4\right)$$  

Drag and Drop

$$f\left(x\right)=-\left(x+2\right)^3\left(x-2\right)^4\left(x+1\right)$$ The root x = 2 has a multiplicity of​

Placeholder

which means it will ​

Placeholder

the x-axis at x = 2.

Drag these tiles and drop them in the correct blank above

4

bounce off

3

cross

Multiple Choice

Which of the following describes the roots of the polynomial function: $$f\left(x\right)=\left(x-3\right)^4\left(x+6\right)^2$$  

• x = -3 with multiplicity 2 and

  x = 6 with multiplicity 4

• x = -3 with multiplicity 4 and

  x = 6 with multiplicity 2

• x = 3 with multiplicity 2 and

  x = -6 with multiplicity 4

• x = 3 with multiplicity 4 and

  x = -6 with multiplicity 2

Multiple Choice

Which of the following describes the roots of the polynomial function: $$f\left(x\right)=\left(x-3\right)^4\left(x+6\right)^2$$  

• Crosses where x = 3 and Bounces where x = -6

• Bounces where x = -3 and Bounces where x = 6

• Bounces where

  x = 3 and Bounces where x = -6

• Bounces where x = 3 and Crosses where x = -6

Multiple Choice

Is the leading coefficient positive or negative?

Is the degree even or odd?

$$f\left(x\right)=\left(x-3\right)^4\left(x+6\right)^2$$  

• Negative

  Even

• Negative

  Odd

• Positive

  Even

• Positive

  Odd

Multiple Choice

Which of the following describes the end behavior of $$f\left(x\right)=\left(x-3\right)^4\left(x+6\right)^2$$  

• Right Arrow Up; Left Arrow Up

• Right Arrow Up; Left Arrow Down

• Right Arrow Down; Left Arrow Down

• Right Arrow Down; Left Arrow Up

Multiple Choice

Which of the following describes the leading coefficient and degree of the function?

• Leading Coefficient Positive

  Degree - Even

• Leading Coefficient Positive

  Degree - Odd

• Leading Coefficient Negative

  Degree - Even

• Leading Coefficient Negative

  Degree - Odd

Multiple Choice

Which of the following describes the leading coefficient and degree of the function?

• Leading Coefficient Positive

  Degree - Even

• Leading Coefficient Positive

  Degree - Odd

• Leading Coefficient Negative

  Degree - Even

• Leading Coefficient Negative

  Degree - Odd

Multiple Choice

Which of the following describes the leading coefficient and degree of the function?

• Leading Coefficient Positive

  Degree - Even

• Leading Coefficient Positive

  Degree - Odd

• Leading Coefficient Negative

  Degree - Even

• Leading Coefficient Negative

  Degree - Odd

Multiple Choice

Which of the following describes the leading coefficient and degree of the function?

• Leading Coefficient Positive

  Degree - Even

• Leading Coefficient Positive

  Degree - Odd

• Leading Coefficient Negative

  Degree - Even

• Leading Coefficient Negative

  Degree - Odd

Multiple Choice

Which of the following describes the leading coefficient of the function?

• positive
• negative

Multiple Choice

Describe the end behavior

$$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow$$ ____

$$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow$$ ____

• -∞
  -∞
• +∞
  -∞
• -∞
  +∞
• +∞
  +∞

Multiple Choice

Describe the end behavior

$$As\ x\rightarrow-\infty,\ f\left(x\right)\rightarrow$$ ____

$$As\ x\rightarrow\infty,\ f\left(x\right)\rightarrow$$ ____

• -∞
  -∞
• +∞
  -∞
• -∞
  +∞
• +∞
  +∞

Multiple Select

Choose all EVEN degree functions

• A

• B

• C

• D

Multiple Select

Choose all functions with a NEGATIVE leading coefficient

• A

• B

• C

• D

Multiple Choice

All polynomials have a range of $$\left(-\infty,\infty\right)$$

• True
• False

Multiple Choice

All polynomials have a domain of $$\left(-\infty,\infty\right)$$

• True
• False

Multiple Choice

How many roots does the function have?

• 2

• 3

• 4

• 5

Multiple Choice

How many intervals of increase does the function have?

• 2

• 0

• 4

• 3

Multiple Choice

What are the intervals of increase?

Remember: Look at the

• (-∞, 2) U (-2, ∞)

• (-2, 2) U (-2, ∞)

• (-∞, -2) U (0.5, ∞)

• (0, 2) U (0.5, ∞)

Multiple Choice

Does the function have an absolute maximum?

• Yes 
• No

Multiple Choice

What is the blue point?

• Absolute Maximum

• Absolute Minimum

• Local Maximum

• Local Minimum

Complex Numbers

Use your calculator :)

Just remember, i² = -1

Multiple Choice

Calculate:
(4 − 7i) − (-3 + 6i)

• 7 − 13i
• 7 − i 
• 1 − 13i
• 1 − i 

Multiple Choice

Calculate:
 (4 + 3i)(4 − 3i)

• 16 − 9i

• 25
• 7
• 8 − 6i

Multiple Choice

What is the simplified form of (-9 + 5i) + (3 -2i)

• -12 + 31i

• -6 + 3i

• -11 + 7i

• 5 - 3i