The graph of a quadratic function has the shape
of a parabola. Parabolas have many applications in engineering and
science. For example, radar, antennas and the paths of projectiles are
parabolic.
Example 15
The rate of a chemical reaction, v, involving the transformation
of one compound into another compound is given by
where x is the concentration of the new compound. What value of x
results in the maximum value of v, and what is the maximum value?
Solution:
So, the maximum value of v is 9 and it occurs when x
= 3.
Example 16
A farmer wants to build a fence around a rectangular paddock using the
straight edge of a canal as one side. She has 400 m of fencing and wants
to enclose the maximum area.
a. If the width of the paddock is x m, express the:
(i) length, l, of the paddock in terms of x
(ii) area, A, of the paddock in terms of x
b. Express A in square completion form.
c. Sketch the graph of A showing all key features.
d. Determine the length and width of the paddock for its area to be
maximised.
Solution:
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