1.3 Maximum Or Minimum Of A Quadratic Function Worksheet - Mcgraw-Hill Education Canada
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91.3
< P1-6 photo of a
large arched bridge,
similar to the one
on page 292 or p
360-361of the “fish”
Maximum or Minimum
book>
of a Quadratic Function
Some bridge arches are defined by quadratic functions. Engineers use these quadratic functions
to determine the maximum height or the minimum clearance under the support of the bridge at a
variety of points. They can give this information to the bridge builders.
A quadratic function can be written in a number of forms. Each form has
different advantages. In all forms, a determines the direction of opening
y
and the shape.
• From the standard form, f (x) 5 ax
bx + c, the y-intercept can be
2
c
identified as c.
r
s
x
0
• From the factored form, f (x) 5 a(x r)(x s), the x-intercepts can be
(h, k)
identified as r and s.
• From the vertex form, y 5 a(x h)
k, the coordinates of the vertex
2
can be identified as (h, k). If a is positive, the minimum value is k. If a
is negative, the maximum value is k.
Investigate a
tools
• graphing calculator
How can you connect different forms of the same quadratic function?
or
• grid paper
Graph each pair of functions.
.
a)
f (x) 5 (x 2)
3 and f (x) 5 x
4x 7
2
2
b)
f (x) 5 (x 3)
4 and f (x) 5 x
6x 5
2
2
f (x) 5 2(x 3)
4 and f (x) 5 2x
12x 22
c)
2
2
d)
f (x) 5 3(x 1)
7 and f (x) 5 3x
6x 4
2
2
.
Why are the graphs of the functions in each pair the same?
How can you rewrite the first equation in each pair in the form of the
3.
second equation?
4.
How can you rewrite the second equation in each pair in the form of
the first equation?
Reflect
5.
How can you use a graph to verify that two quadratic
functions in different forms represent the same function? If you are
using a graphing calculator, is it enough to observe that the graphs
look the same on your screen? Explain.
1.3 Maximum or Minimum of a Quadratic Function • MHR 5
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