Forms of Quadratic Equations
standard form
vertex form
intercept form
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� 🡪 Area Maximization
🡪 Modelling � Suspension Bridges
Area Maximization
If you have a fixed perimeter of 16 for a rectangle, �then what dimensions will maximize the area ?
Today: FOUR PROBLEMS
Maximizing the area �of a Sports Field
Modelling a �Suspension Bridge
Maximizing�the area of�an enclosure
vertex
Problem 1
300 meters of fence is used to plot out a rectangular piece of land along a river.� �1. Write an equation for the length of fence.�2. Use your equation to rewrite the � length (l) in terms of w.�3. Write an equation for the area of the land � in terms of w. A = �
y
300 = 2w + l
l = 300 – 2w
300 – 2w
A = w(300 – 2w)
A = wl
Find the x-intercepts and use them �and the vertex to sketch a graph�of the area function.
Problem 2
l
w
You have 200 m. of fence and �create the enclosure shown. ��1) Write an equation for area � using l and w.��2) Write an equation to show the � total length of fencing.��3) Combine the two equations to � write an equation for area � in terms of l only.
4) Find the values of l and w � that lead to the maximum area.� What is this area?�
l
w
l
l
w
A = (l)(w)
200 = 3l + 2w
You have 200 m. of fence and �create the enclosure shown. ��1) Write an equation for area using l and w.��2) Write an equation to show the total length of fencing.��3) Combine the two equations to write an equation � for area in terms of l only.
�4) Find the values of l and w that lead to the � maximum area. What is this area?�
w
l
l
w
l
vertex
Problem 3
Problem 4
Problem 4
Back to the Golden Gate Bridge…