U4L8 More Modeling Integrated Math 9A
Day 8 Quadratics – More Modeling
Today we will finally look at how quadratic functions are useful in lots of every day scenarios. In particular we
will see how x-intercepts and the vertex have very important applications. Today we will also focus more on
creating the equation given information.
1. A hauling company needs to determine whether a wide load trailer can be moved along a highway that passes under
a bridge with an opening in the shape of a parabolic arch that is 12 m wide at the base and 6 m high in the center. If
the trailer is 9 m wide and 3.2 m tall, will it fit under the bridge? Make a diagram of this problem and justify your
answer.
2. The human cannonball is an act where a performer is launched through the air. The height of the performer
can be modeled by h x = −0.007x ! + x + 20, where h(x) is the height in feet and x is the horizontal
distance from the cannon traveled in feet. The circus act wants to launch the performer directly over the
main tent.
a. If the performer wants at least 5 feet of vertical clearance over the tent, and assuming the performer
reaches her maximum height directly above the tent, how tall can then tent. Hint: Draw a detailed
picture of this situation - think about the location of the vertex and the intercepts.
b. How far from the tent’s central pole should the cannon be placed?
U4L8 More Modeling 3. On a trip to St. Louis you visit the Gateway Arch. You learn the following specs about the arch:
• The highest point is 185 meters.
• From one end to the other at the bottom the arch is 162 meters.
• The archway is perfectly symmetrical.
a. Sketch a graph of the arch and create a quadratic equation that models this arch.
b. An airplane with a wingspan of 40 meters tries to fly through the arch at an altitude of 170 meters.
Could the plane possibly make it? Justify your answer.