1.3 Maximum Or Minimum Of A Quadratic Function Worksheet - Mcgraw-Hill Education Canada Page 7
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1
2
3
4
5
6
7
8
9Communicate Your Understanding
C
In one step of completing the square, you divide the coefficient of x by 2 and square the
result. Why?
C
How are the functions f (x) 5 4x(x 3), g(x) 5 4x(x 3) 2, and h(x) 5 4x(x 3) 1
related? Explain using words and diagrams.
Ryan does not understand the concept of partial factoring to determine the vertex. Use the
C3
function y 5 3x
9x 17 to outline the technique for him.
2
A
Practise
Use Technology
4.
Use a graphing calculator
For help with questions 1 and 2, refer to
to verify your answers to questions 2 and 3.
Example 1.
B
Connect and Apply
Complete the square for each function.
.
a)
y 5 x
2
4x
For help with questions 5 and 6, refer to
Example 3.
b)
f (x) 5 x
7x 11
2
c)
g(x) 5 x
3x 1
2
An electronics store sells an average of
5.
60 entertainment systems per month at an
d)
y 5 x
11x 4
2
average of $800 more than the cost price.
e)
f (x) 5 x
13x 2
2
For every $20 increase in the selling price,
f)
y 5 x
9x 9
2
the store sells one fewer system. What
amount over the cost price will maximize
.
Determine the vertex of each quadratic
profit?
function by completing the square. State if
the vertex is a minimum or a maximum.
6.
Last year, a banquet hall charged $30 per
a)
f (x) 5 x
10x 6
2
person, and 60 people attended the hockey
banquet dinner. This year, the hall’s
f (x) 5 2x
12x 16
b)
2
manager has said that for every 10 extra
f (x) 5 3x
6x 1
c)
2
people that attend the banquet, they will
f (x) 5 x
12x 5
d)
2
decrease the price by $1.50 per person.
_
_
f (x) 5 1
x 3
x
e)
2
What size group would maximize the
2
2
_
_
_
profit for the hall this year?
f (x) 5 2
16
x 25
f)
x
2
3
3
3
For help with question 7,
Reasoning and Proving
For help with question 3, refer to Example 2.
refer to Example 4.
Representing
Selecting Tools
3.
Use partial factoring to determine the
7.
A ball is kicked into
Problem Solving
vertex of each function. State if the vertex
the air and follows
Connecting
Reflecting
is a minimum or a maximum.
a path described by
Communicating
f (x) 5 3x
6x 11
a)
2
h(t) 5 4.9t
6t 0.6,
2
where t is the time, in seconds, and h is
b)
f (x) 5 2x
2
8x 3
_
f (x) 5 1
the height, in metres, above the ground.
c)
x
3x 8
2
2
Determine the maximum height of the ball,
_
f (x) 5 5
d)
x
5x 10
2
to the nearest tenth of a metre.
3
e)
f (x) 5 0.3x
3x 6
2
f)
f (x) 5 0.2x
2.8x 5.4
2
1.3 Maximum or Minimum of a Quadratic Function • MHR 3
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