Unit 1 Test Review: Quadratic Functions

Unit 1 Test Review: Quadratic Functions

Multiple Choice

Which of the following functions does not have a minimum?

• 
  

  $-\left(x+1\right)\left(x+7\right)$

• $3\left(x-5\right)^2+1$

• $x^2-50x+100$

• $4x^2-x-9$

Multiple Choice

The income in dollars from admission charges for a fund raiser is represented by $40p-4p^2$  , where p is the admission charge in dollars. How much should the admission charge be to maximize profit?

• $1

• $100

• $10

• $5

Multiple Choice

The path of a foam ball shot from a toy gun can be described by the equation , where  $f\left(x\right)=-x^2+4x-1$  is the height of the foam ball and x is the number of seconds that have passed since the toy gun’s trigger was released. Which of the following points shows the extremum for the function?

• (0,-1)

• (2,3)

• (-2,3)

• (2, -3)

Multiple Choice

Dalco Manufacturing estimates that its weekly profit, P can be approximated by the formula  $P=-3x^2-6x+12$ , where x is the number of units produced per week. Find the maximum weekly profit.

• $1

• $15

• $12

• $0

Multiple Choice

The function  $y=-14x^2+196$  models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground. Round to the nearest hundredth of a second.

• 196 seconds

• -3.742 seconds

• 3.742 seconds

• 14 seconds

Multiple Choice

Given the quadratic function, $q\left(x\right)=-2\left(x+5\right)^2-8\$  

 identify the vertex and determine whether it is a minimum or maximum.

• (5, -8), maximum

• (5, -8) minimum

• (-5, -8), maximum

• (-5, -8), minimum

Multiple Choice

What characteristic of a parabola can be easily identified when the factored form of a quadratic is given?

Factored Form: (x+p)(x+q)=0

• extremum

• vertex

• x-intercept(s)

• y-intercept

Multiple Choice

What characteristic of a parabola can be easily identified when it is in vertex form?

Vertex Form: $y\ =\ a\ \left(x\ -h\right)^2+k$  

• extremum

• vertex

• x-intercept(s)

• y-intercept

Multiple Choice

What is the vertex form of the function: $f\left(x\right)=x^2-4x+1$  

•  $\left(x-2\right)^2-3$  

•  $\left(x+2\right)^2-3$  

•  $\left(x-2\right)^2+3$  

•  $\left(x+2\right)^2+3$  

Multiple Choice

If the value of a is negative and the vertex is at (12, –2), then how many x-intercepts will the graph have?

• 2

• not enough information

• 0

• 1

Multiple Choice

What is the vertex of the function

 $f\left(x\right)=\left(x-5\right)\left(x+3\right)$  ?

• (0,-15)

• (1,-16)

• (5,0)

• (-3,0)

Multiple Choice

Solve

 $x^2+9x=10$  for x. 

• x =10 or x = -1

• x=0

• x=-10

• x=-10 or x =1

Multiple Choice

What are the zeros of the function  $f\left(x\right)=x^2-81?$  

• 9

• -9

• -9,9

• no solution

Multiple Choice

What are the roots of the equation:

 $2x^2-14x+20$  ?

• x=2 or x=5

• (3.5,-4.5)

• (0,20)

• x=-2 or x = -5

Multiple Choice

Solve $4x^2-7x-15$  .

• x = -1.25, 3

• x = 0, -15

• x = 1.25, -3

• x = 0, 15

Multiple Choice

What are the complex solutions of the equation 

 $4x^2-3x+1=0$  .

•  $\left(\frac{3+i\sqrt{7}}{8},\frac{3-i\sqrt{7}}{8}\right)$  

•  $\left(\frac{-3+i\sqrt{7}}{8},\frac{-3-i\sqrt{7}}{8}\right)$  

Multiple Choice

Find a quadratic function to model the values in the table.

• $2x^2-2x-2$

• $2x^2-2x+2$

• $2x^2+2x-2$

• $2x^2+2x+2$

Multiple Choice

A baseball is hit so that its height in feet, t seconds after it is hit, can be modeled by the function h(t) =  $-8t^2+36t-2$  . A hawk takes off from its nest 28 feet above the ground at the same time that the player hits the baseball. The hawk’s flight can be modeled by the function h(t) =  $27-t$ . After how many seconds do the hawk and baseball first achieve the same height? What is that height? (Hint: first intersection)

• 3.625 seconds and 23.375 feet off the ground

• 1 second and 26 feet off the ground

• 2.25 seconds and 38.5 feet off the ground 

• 2.1 seconds and 30 feet off the ground

Multiple Choice

Use the graph to determine the real solution(s) to the system of equations, if any exist.

• no real solutions

• (0,-6)

• (-3,0)

• (0,3)

Multiple Choice

Given the graph for one quadratic function and the table of values for another, determine which has a smaller y-intercept.

• f(x)

• g(x)