On my planet, the whole day lasts nine years. The day lasts 4.5 years of incredible heat, with glaciers from the night providing water. The night starts with the sunset, during which violent tornadoes occur and enters into the night lasting four and a half years before another set of tornadoes and then the cycle restarts. Animals migrate to survive these conditions but plants cannot do this. Many plants other than trees just spread their seeds and die during the winter in the real world. How would annual plants such as trees and cacti survive tornadoes as well as four and a half years of darkness and cold?
Most plants would rely on seeds, and would have multiple cycles during the 39,420 hours of daylight. The seeds would probably have some temperature sensitivity so as to not germinate just before dusk.
Other plants might have hardened cores, where most of the plant could go dormant and lose most of it's water to prevent cell rupture, while a small place in the center would stay alive.
Trees could grow very deep roots to store energy harvested during the long day time, and at night would use geothermal heat from deep underground to keep from freezing completely. Because trees grow slower, they might not depend on seeds, but instead sprout something like basal shoots, which would form into new trees, pulling energy and warmth from the parent until they can put down their own deep roots and become self sufficient.
One fun idea is a plant that "migrates". It likes a certain light level, and doesn't do well in bright sunlight or in darkness. It's area is in the higher latitudes where the sun is not directly overhead. It's a creeper and is constantly growing toward the best light, meaning that it's growth is mainly in one direction, following the sun. As it's old growth moves closer to dusk it dies off and rots, putting nutrients back into the soil for it to utilize the following day as the planet rotates back to the relative location of the plant.
Luckily for the plant, there are no large bodies of water at that latitude that might block it's path.
I'd like to point out that during that 4.5 year day these plants are going to have to keep growing, maybe even go thorugh multiple fertility phases, otherwise everyone would simply starve (imagine if all plants only produced fruit once in 4 years).
This implies that energy stored is consumed over time, so I'm not sure how much energy they will have available for the start of night.
That being said, here's some ideas:
These plants just store a lot of energy, then go into hybernation mode. They husband their resources, and many of them survive the long night.
Multiple Ways of Producing Energy
There are plants which thrive in darkness. Many plants on this planet might have evolved a sort of dual energy production system. One chlorophyll based, one similar to what mushrooms utilize, or maybe even carnivorous (eating insects, or small mammals).
Circle Of Life
Some plants may indeed die during the long night, yet leave their seeds behind to bloom when the sun comes up again. The tornadoes themselves may carry these seeds over from the day-side.
Perennials/Weird Energy Storage
Some plants may develop ways to store energy in massive underground root systems which they all draw power from (think of Avatar and the way in which all trees were connected).
From plants'perspective, that's not so different from Earth as it could seem.
In most climates in Earth, plants undergo periods of inactivity for several months a year, and in certain desert climates inactivity can even take years - until it rains. In those resting periods plants can remain in several forms: seeds, underground organs, or even the whole plant in a latency state. There is even a widely used classification of plant life forms based on how they deal with where buds remain in the disfavourable season.
The nine years cycle might be harder -colder, longer- than anything on Earth, but it's not very different from we have here, and some strategies that work for Earth plants (seeds?) are likely to work in the OP's planet.
My first thought was: It's Mushroom time!
Your photosynthetic plants would go through multiple cycles during the day, adapted for unrelenting sunlight. Trees and woody plants would have to hibernate, at night, and store enough to stay alive until the sun came back. The rest would just use seeds, and wait for light.
At night there would be fungus, and everything else that grows without light. Probably a lot that would be killed by light. There'd be lots of dead plants for them to use as nutrients. The woody plants of daytime would need some protection during the night, to keep from getting eaten.
Annual plants could certainly make it with seeds that lie dormant during the "night", or winter. Sub-zero night temperatures can aid in prolonging seed viability while dormant. Even on Earth, plants like Lithops can produce seeds which remain viable for a few years without freezing.
At such a slow rotation , convection cells create strong winds which may also assist in seed dispersal. It's almost like tidal locking. Surface winds blow towards the bright side, so that each generation of seeds takes its part in the perpetual chase of the sun.
Migrating animals can easily migrate to the "twilight zone" and beyond. On their way, they eat fruits and disperse their seeds.
Perennial plants have different strategies:
1- blur the boundary between plant and animal. Give your plant the ability to move, and swim if necessary. After all, it's a SLOW rotation!
2- Remain active through the winter because oceans and atmosphere bring some heat to the other side. The atmosphere should be thick enough. They can harness wind power when light is absent: think of electrostatics due to wind friction.
3- Give them the ability to remain dormant if everything else fails. The plant starts to grow early. It has 4.5 Earth years to grow ans store enough sugars and minerals. When it's too cold, they hibernate.
Dealing with tornadoes: annuals can bend like grass. Perennials must store food in big roots and very short and stocky trunks. Barrel-cactus shape or even dome-shaped are best.