Roots of a Quadratic Function

Short Quiz in Math 9 characterizes the roots of a quadratic equation using the discriminant

Short Quiz in Math 9 describes the relationship between the coefficients and the roots of a quadratic expression

A1.AREI.4* Solve mathematical and real-world problems involving quadratic equations in one variable. (Note: A1.AREI.4a and 4b are not Graduation Standards.) a. Use the method of completing the square to transform any quadratic equation in 𝑥 into an equation of the form (𝑥 − ℎ)2 = 𝑘 that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex

Create a quiz with the following questions and answersConvection is… The rising motion of warm air A large volume of air A boundary between two different air masses The weight of the Earth’s atmosphere over an area What are isobars? Storms with strong winds, heavy rains, lightning, and thunder Lines on a map to show high and low pressure The study of elevation This front is associated with thunderstorms, heavy rain, snow, and cooler temperatures. Warm front Stationary front Cold front Occluded front What is a barometer? A tool used to measure temperature An instrument used to measure wind speed An instrument used to measure humidity An instrument used to measure air pressure What is a tornado? Storms with strong winds, heavy rains, lightning, and thunder Large, rotating tropical weather systems A rapidly spinning column of air that has touched the ground What is topography? The study of elevation Lines on a map to show high and low pressure The condition of the atmosphere at a given place and time What are air masses? Large, rotating tropical weather systems The study of elevation A large volume of air with the same temperature What is transpiration? The process of a liquid’s surface changing into a gas The process of a gas changing into a liquid The movement of water through the soil The process of water vapor being released by plants. What is nitrification? The process bacteria use to convert nitrogen gas into ammonium ions The process of turning ammonium ions into nitrites and nitrates. The uptake of nitrates in the soil by the roots of plants. The process of turning nitrates into nitrogen gas Fun Fact: Carbon makes up ___ of your mass. 30% 18% 50% 6% What are the reactants of photosynthesis? Carbon dioxide and water Glucose and oxygen What are the reactants of cellular respiration? Carbon dioxide and water Glucose and oxygen What is a storm surge? Flooding caused by hurricanes Region of air where the air pressure is low Any product of the condensation of water vapor High pressure is… A region of air where the air pressure is greater than that of the surrounding area A region of air where the air pressure is lower than that of the surrounding area. Low pressure is… A region of air where the air pressure is greater than that of the surrounding area A region of air where the air pressure is lower than that of the surrounding area. What causes global winds? Photosynthesis The process carbon goes through Uneven heating of the Earth What can humans do to reduce carbon emissions? We can use renewable energy (ex. solar power) We can use non-renewable energy (ex. fossil fuels) Carbon can form stable bonds with many elements and and makes up the backbone of major macromolecules: carbohydrates, proteins, lipids, and ___ Nucliec acids Glucose Oxygen Nitrogen What weather is associated with low-pressure systems? Bad weather (ex. Cloudy weather) Good weather (ex. Sunny weather) What is fossilization? The burning of fossil fuels The process where fungi and bacteria decompose dead organisms Dead organisms form fossil fuels over thousands and millions of years What is the first step in the formation of tornadoes? Rising air from the ground pushes up on the swirling air and tips it over A large thunderstorm occurs in a cumulonimbus cloud The funnel grows longer and stretches towards the ground The funnel of swirling air begins to suck up more warm air from the ground What is the difference between thunderstorms and regular storms? Thunderstorms have thunder while regular storms don’t Regular storms have thunder while thunderstorms don’t There is no difference What are hurricanes? Rapidly spinning columns of air touch the ground Large, rotating tropical weather systems Storms with strong winds, heavy rains, lightning, and thunderstorms What is not a hurricane fact? They are the most powerful storms on earth They have an average wind speed of 120-180 km/h They lose their power when they travel over cooler waters or land Storm surges cause the most damages What is the difference between weather and climate? Weather is long-term while climate is short-term Climate is long-term while weather is short-term There is no difference

Cohesion and Adhesion Water molecules stick to each other as a result of hydrogen bond- ing. An attractive force that holds molecules of a single substance together is known as cohesion. Cohesion due to hydrogen bonding between water molecules contributes to the upward movement of water from plant roots to their leaves. Related to cohesion is the surface tension of water. The cohe- sive forces in water resulting from hydrogen bonds cause the mol- ecules at the surface of water to be pulled downward into the liquid. As a result, water acts as if it has a thin “skin” on its sur- face. You can observe water’s surface tension by slightly overfill- ing a drinking glass with water. The water will appear to bulge above the rim of the glass. Surface tension also enables small crea- tures such as spiders and water-striders to run on water without breaking the surface. Adhesion is the attractive force between two particles of differ- ent substances, such as water molecules and glass molecules. A related property is capillarity (KAP-uh-LER-i-tee), which is the attrac- tion between molecules that results in the rise of the surface of a liquid when in contact with a solid. Together, the forces of adhe- sion, cohesion, and capillarity help water rise through narrow tubes against the force of gravity. Figure 2-11 shows cohesion and adhesion in the water-conducting tubes in the stem of a flower. Temperature Moderation Water has a high heat capacity, which means that water can absorb or release relatively large amounts of energy in the form of heat with only a slight change in temperature. This property of water is related to hydrogen bonding. Energy must be absorbed to break hydrogen bonds, and energy is released as heat when hydrogen bonds form. The energy that water initially absorbs breaks hydro- gen bonds between molecules. Only after these hydrogen bonds are broken does the energy begin to increase the motion of the water molecules, which raises the temperature of the water. When the temperature of water drops, hydrogen bonds reform, which releases a large amount of energy in the form of heat. Therefore, during a hot summer day, water can absorb a large quantity of energy from the sun and can cool the air without a large increase in the water’s temperature. At night, the gradually cooling water warms the air. In this way, the Earth’s oceans stabilize global temperatures enough to allow life to exist. Water’s high heat capac- ity also allows organisms to keep cells at an even temperature despite temperature changes in the environment. As a liquid evaporates, the surface of the liquid that remains behind cools down. A relatively large amount of energy is absorbed by water during evaporation, which significantly cools the surface of the remaining liquid. Evaporative cooling prevents organisms that live on land from overheating. For example, the evaporation of sweat from a person’s skin releases body heat and prevents over- heating on a hot day or during strenuous activity. Adhesion Cohesion Hydrogen bonds Cohesion, adhesion, and capillarity contribute to the upward movement of water from the roots of plants. FIGURE 2–11 www.scilinks.org Topic: Hydrogen Bonding Keyword: HM60777 mb06se_cols03.qxd 5/18/07 10:47 AM Page 41 42 CHAPTER 2 Density of Ice Unlike most solids, which are denser than their liquids, solid water is less dense than liquid water. This property is due to the shape of the water molecule and hydrogen bonding. The angle between the hydrogen atoms is quite wide. So, when water forms solid ice, the angles in the molecules cause ice crystals to have large amounts of open space, as shown in Figure 2-12. This open space lattice structure causes ice to have a low density. Because ice floats on water, bodies of water such as ponds and lakes freeze from the top down and not the bottom up. Ice insulates the water below from the cold air, which allows fish and other aquatic crea- tures to survive under the icy surface.

Land preparation •Carrots can be planted in beds. •The beds should be prepared before planting. (a)digging: this is done using a hoe or a spade so as to loosen the soil. •During digging , remove roots and stems of weeds. (b) manuring: add 2kg of well rotten manure per square metre. •Work the manure deeply into the soil so that the roots of the carrots do not come into directly contact with manure. •Improperly incorporated manure causes development of carrots that have side roots. •this condition is called forking. Planting •Carrots are planted in beds where they will mature. •Water the bed a day before planting. •Mark the rows 30cm apart. •Carrots seeds are very small, therefore due to their size sow the seeds thinly along the rows. •Rub the seeds between your fingers as you sow. •Cover the seeds with fine sand. •The bed can be covered with grass so that the soil remain moist. •Water the bed soon after sowing using a watering can fitted with a fine rose. Caring for carrots (a) Thinning: is when you remove some of the baby plants in a row to free up space for the rest so that they can grow to full size. • Thinning in carrots is usually done two weeks after germination. • Thin out to leave a spacing of 4 -6 cm from each plant. (b) Watering: If carrots are not watered enough they will not grow fast. • Therefore carrots need a steady supply of water to keep the soil moist during the growing period. (c) Weeding: weeds are removed by hand, especially those in the rows. (d) Top dressing: carrots are usually not top dressed. •Fertilizer can only be applied after one has noticed leaves turning yellow. (e) Pest and disease control: aphids and nematodes attack carrots. •Dimethoate is used to control aphids. Harvesting carrots •Carrots are harvested 2 to 3 months after planting. •Bigger ones are harvested first inorder to leave more room for the young seedlings to develop. •Water the bed first the lift the carrots by hand. •A garden fork can also be used to loosen the soil, then pull up by hand. •The carrots can then be tied into bunches of 5 – 7 carrots

Which of these is a flowering plant? a) Fern b) Rose c) Moss d) Algae What type of plant does not produce flowers? a) Tulip b) Dandelion c) Pine Tree d) Orchid Which of these plants grows in water? a) Cactus b) Lotus c) Oak Tree d) Grass What do we call plants that have seeds inside fruits? a) Non-seed plants b) Seedless plants c) Flowering plants d) Root plants Which of these is an example of a desert plant? a) Sunflower b) Cactus c) Bamboo d) Willow Which type of plant usually grows in land? a) Aquatic plants b) Desert plants c) Air plants d) All of the above What part of the flowering plant produces seeds? a) Roots b) Leaves c) Flowers d) Stem Which of the following plants is non-flowering? a) Tulip b) Fern c) Marigold d) Daisy What type of environment do water plants thrive in? a) Desert b) Ocean c) Mountain d) City Which of these plants is adapted to grow in the air? a) Orchid b) Maple c) Pine d) Wheat What type of seed does a watermelon have? a) Hard seed b) Soft seed c) No seed d) Air seed Which plant grows in both land and water? a) Fern b) Duckweed c) Oak Tree d) Sunflower What is the main function of a flower? a) To produce leaves b) To make seeds c) To grow roots d) To collect water Which plant is NOT typically found in a desert? a) Cactus b) Saguaro c) Palm Tree d) Maple Tree Which of the following plants has flowers? a) Pine b) Rose c) Moss d) Grass

A solution is composed of a solute dissolved in a solvent. In the sugar water described in Figure 5-1, the solute was sugar and the solvent was water, and the solute molecules diffused through the solvent. It is also possible for solvent molecules to diffuse. In the case of cells, the solutes are organic and inorganic compounds, and the solvent is water. The process by which water molecules diffuse across a cell membrane from an area of higher concentration to an area of lower concentration is called osmosis (ahs-MOH-sis). Because water is moving from a higher to lower concentration, osmosis does not require cells to expend energy. Therefore, osmosis is the passive transport of water. Direction of Osmosis The net direction of osmosis depends on the relative concentra- tion of solutes on the two sides of the membrane. Examine Table 5-1. When the concentration of solute molecules outside the cell is lower than the concentration in the cytosol, the solution outside is hypotonic to the cytosol. In this situation, water diffuses into the cell until equilibrium is established. When the concentration of solute molecules outside the cell is higher than the concentration in the cytosol, the solution outside is hypertonic to the cytosol. In this situation, water diffuses out of the cell until equilibrium is established. Observing Diffusion Materials 600 mL beaker, 25 cm dialysis tubing, funnel, 15 mL starch solution (10 percent), 20 drops Lugol’s solution, 300 mL water, 100 mL graduated cylinder, 20 cm piece of string (2) Procedure 1. Put on your disposable gloves, lab apron, and safety goggles. 2. Pour 300 mL of water in the 600 mL beaker. 3. Add 20 drops of Lugol’s solution to the water. CAUTION: Lugol’s solution is a poison and eye and skin irritant. 4. Open the dialysis tubing, and tie one end tightly with a piece of string. 5. Using the funnel, pour 15 mL of 10 percent starch solution into the dialysis tubing. 6. Tie the other end of the dialysis tubing tightly with the second piece of string, forming a sealed bag around the starch solution. 7. Place the bag into the solution in the beaker, and observe the setup for a color change. Analysis What happened to the color in the bag? What happened to the color of the water around the bag? Explain your observations. Quick Lab www.scilinks.org Topic: Osmosis Keyword: HM61090 mb06se_homs01.qxd 11/27/07 8:52 AM Page 98 HOMEOSTASIS AND CELL TRANSPORT 99 When the concentrations of solutes outside and inside the cell are equal, the outside solution is said to be isotonic to the cytosol. Under these conditions, water diffuses into and out of the cell at equal rates, so there is no net movement of water. Notice that the prefixes hypo-, hyper-, and iso- refer to the relative solute concentrations of two solutions. Thus, if the solution outside the cell is hypotonic to the cytosol, then the cytosol must be hyper- tonic to that solution. Conversely, if the solution outside is hypertonic to the cytosol, then the cytosol must be hypotonic to the solution. Water tends to diffuse from hypo- tonic solutions to hypertonic solutions. How Cells Deal with Osmosis Cells that are exposed to an isotonic external environment usually have no difficulty keeping the movement of water across the cell membrane in balance. This is the case with the cells of ver- tebrate animals on land and of most other organ- isms living in the sea. In contrast, many cells function in a hypotonic environment. Such is the case for unicellular freshwater organisms. Water constantly diffuses into these organisms. Because they require a relatively lower concentration of water in the cytosol to function normally, unicel- lular organisms must rid themselves of the excess water that enters by osmosis. Some of them, such as the paramecia shown in Figure 5-2, do this with contractile vacuoles (kon-TRAK-til VAK-y ̄ ̄o ̄ ̄o-OL), which are organelles that remove water. Contractile vacuoles collect the excess water and then contract, pumping the water out of the cell. Unlike diffusion and osmosis, this pumping action is not a form of passive trans- port because it requires the cell to expend energy. Copyright © by Holt, Rinehart and Winston. All rights reserved. (a) (b) Vacuole filling with water Vacuole contracting TABLE 5-1 Direction of Osmosis Condition External solution is hypotonic to cytosol External solution is hypertonic to cytosol External solution is isotonic to cytosol Net movement of water into the cell out of the cell none H2O H2O H2O H2O H2O H2O The paramecia shown below live in fresh water, which is hypotonic to their cytosol. (a) Contractile vacuoles collect excess water that moves by osmosis into the cytosol. (b) The vacuoles then contract, returning the water to the outside of the cell. (LM 315) FIGURE 5-2 100 CHAPTER 5 (a) HYPOTONIC Cell walls (b) HYPERTONIC (a) ISOTONIC (b) HYPOTONIC (c) HYPERTONIC Other cells, including many of those in multicellular organisms, respond to hypotonic environments by pumping solutes out of the cytosol. This lowers the solute concentration in the cytosol, bring- ing it closer to the solute concentration in the environment. As a result, water molecules are less likely to diffuse into the cell. Most plant cells, like animal cells, live in a hypotonic environ- ment. In fact, the cells that make up plant roots may be surrounded by water. This water moves into plant cells by osmosis. These cells swell as they fill with water until the cell membrane is pressed against the inside of the cell wall, as Figure 5-3a shows. The cell wall is strong enough to resist the pressure exerted by the water inside the expanding cell. The pressure that water molecules exert against the cell wall is called turgor pressure (TER-GOR PRESH-er). In a hypertonic environment, water leaves the cells through osmosis. As shown in Figure 5-3b, the cells shrink away from the cell walls, and turgor pressure is lost. This condition is called plasmolysis (plaz-MAHL-uh-sis), and is the reason that plants wilt if they don’t receive enough water. Some cells cannot compensate for changes in the solute con-

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