Unit 1 Test Review: Quadratic Functions

Which of the following functions does not have a minimum?

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?

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?

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.

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.

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.

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

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

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

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

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

What is the vertex of the function

Solve

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

What are the roots of the equation:

Solve $4x^2-7x-15$  .

What are the complex solutions of the equation 

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

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)

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

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