Helpful Tip when solving for Word Problems are....

 

1) Read

2) Plan

3) Solve

4) Check 

5) Conclude

 

 

Since you can idenify how to solve for the zeros, you are ready to do word problems!

 

Example 1: Shawn Mendes models his profit for his tour 'Handwritten', P dollars, by the equation P= -11(t-50)^2+10571, where t dollars is the cost per ticket. 

 

 

a) What price should he charge to maximize his profit? What is the maximum profit? [Vertex]

*Remember when you hear maximize and maximum, the question is always asking for the Vertex*

Vertex: (50,10571)

     Therefore, the price he should charge to maximize his profit is $50, and his maximum profit is $10571.

 

b) What will be his profit if the tickets were free? [T=0]

*Since it is asking what the profit would be it the tickets were free, it means to find the value of P*

P= -11(t-50)^2+10571

P= -11(0-50)^2+10571

P=-11(-50)^2+10571

P= -11(2500)+10571                      Therefore, if Shawn makes his tickets free then he would lose

P= -27500+10571                                  $16930

P= -16930

 

 

 

c) How much should he charge per ticket to break even? [P=O]

*Asking you to find the t value, so you sub in P=0*

P= -11(t-50)^2+10571

0= -11(t-50)^2+10571

-10571= -11(t-50)

   -11      -11

961= (t-50)^2

t-50= (+)(-)√961

 

 

 

 

 

 

 

 

 

Example 2: The height of a football is thrown following the path, h=-5(t-2)^2+40.5. Where h is the height is meters, and t is time in seconds. 

 

a) What is the maximum height of the football? [Vertex]

Vertex(2,40.5) 

Therefore, the maximum height of the football is 40.5m

 

b) How long does it take for the football to reach its maximum height?

Therefore, it takes the football 2 seconds to reach its maximum height.

 

c) What was the initial height of the football when it was thrown?

*Asking for the height, so you sub t=0*

 

h= -5(t-2)^2+40.5

h=-5(0-2)^2+40.5                             Therefore, the initial height of the football thrown is 20.5 m 

h= -5(-2)^2+40.5

h=-5(4)+40.5

h= -20+40.5

h= 20.5

 

d) How long was the football in the air?

*Asking for the t value, so sub h=0*

h= -5(t-2)^2+40.5

0=-5(t-2)^2+40.5

-40.5=-5(t-2)^2

  -5      -5

8.1=(t-2)^2

t-2= (+)(-)√8.1

 

 

 

 

 

 

 

e) What is the height of the football at 1 second?

[Sub t=0 and find for the height]  

h= -5(t-2)^2+40.5

h=-5(1-2)^2+40.5

h=-5(-1)^2+40.5

h= -5(1)+40.5                  Therefore, the height of the football after 1 second is 35.5m.

h=-5+40.5

h= 35.5 

 

 

 

 

 

Now its practice:

 

1) The height, h, in metres, of a soccer ball, t seconds after being thrown can be modelled by the equation h= -0.10(t-4)^3+6

 

a) What is the height of the soccer ball thrown after 4 seconds after it is thrown?

 

b) What is initial height of the soccer ball?

 

c) When will the soccer ball reach the ground?

 

 

2) Camila is selling sunglasses. Let p represent the profit and let s represent the selling price. The profit can be modelled by the equation: P -6(s-30)^2+2000

 

a) What is the selling price that will maximize profits? [Vertex]

 

b) What is the selling price when profits equal zero (x- intercepts)

 

 

 

VERTEX FORM EXIT TICKET[OPTIONAL]