Solving “Real Life Problems”
Solving “Real Life Problems”
Quadratic Functions
Ex. 1 The profit in dollars of a shoe company is given by [pic]
where x is the amount of money spent on advertising in dollars.
a) Make a table of values and graph the function.
b) What is the maximum profit?
c) What amount of advertising produces the maximum profit?
d) What amount of advertising produces zero profit?
e) Factor and solve the function[pic] to find the roots.
[pic]
Questions
1. A ball is thrown up into the air at a speed of 5 m/s. The height of the ball in metres is given by the [pic] where t is the time since the object is thrown.
a) Make a table of values and graph the function.
b) What is the maximum height of the ball?
c) At what time does the ball reach its maximum height?
d) At what time does the ball hit the ground?
e) Factor and solve the function [pic] to find the roots.
2. The profit in dollars of a shoe company is given by [pic] where x is the amount of money spent on advertising in dollars.
a) Make a table of values and graph the function.
b) What is the maximum profit?
c) What amount of advertising produces the maximum profit?
d) What amount of advertising produces zero profit?
e) Factor and solve the function [pic] to find the roots.
3. A ball is thrown up into the air at an angle. The height of the ball in metres is given by the [pic] where x is the distance forward in metres.
a) Make a table of values and graph the function.
b) What is the maximum height of the ball?
c) How far does the ball travel forward before it reaches the ground?
e) Factor and solve the function [pic] to find the roots.
4. The profit in dollars of a ice cream company is given by [pic] where T is the amount of money spent on advertising in dollars.
a) Make a table of values and graph the function.
b) What is the maximum profit?
c) What is the temperature that produces the maximum profit?
d) What temperature produces zero profit?
e) Factor and solve the function [pic] to find the
roots.
Instructions for excel
1) Open Excel: Go to START > PROGRAMS > MICOSOFT EXCEL
2) Make a table of values in Excel
|Advertising, x ($) |Profits, P |
| |($) |
|0 |=-5*A2^2+550*A2-5000 |
|10 | |
|20 | |
|30 | |
|40 | |
|50 | |
|60 | |
|70 | |
|80 | |
|90 | |
|100 | |
a) Enter the titles in columns A and B.
b) Enter the x values (Advertising) in column A as shown.
c) Enter the formula for Profit in column B as shown.
d) Copy the formula into the cells below.
|Advertising, x ($) |Profits, P |
| |($) |
| |-5000 |
|10 |0 |
|20 |4000 |
|30 |7000 |
|40 |9000 |
|50 |10000 |
|60 |10000 |
|70 |9000 |
|80 |7000 |
|90 |4000 |
|100 |0 |
e) Highlight the entire table.
f) Create a graph by going to
INSERT > CHART > XY Scatter > Next
Create a neat well labelled graph by right
clicking on different parts of the graph. (axis,
point, grid lines and chart area)
[pic]
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