5 4 Quadratic Models Using Vertex Form The
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5. 4 Quadratic Models Using Vertex Form � The following graph shows bakery profits from bread sales. How do you determine the equation of the quadratic relation from its graph?
Determine Equation from Graph �
Example � The amount of gasoline that a car consumes depends on its speed. Below is the relationship between speed and fuel consumption for a particular car. Speed (km/h) 10 20 30 40 50 60 70 80 90 100 110 120 Gas Consumed (L/100 km) 9. 2 8. 1 7. 4 7. 2 6. 4 6. 1 5. 9 5. 8 6. 0 6. 3 7. 5 8. 4
Example Speed (km/h) 10 20 30 40 50 60 70 80 90 100 110 120 Gas Consumed (L/100 km) 9. 2 8. 1 7. 4 7. 2 6. 4 6. 1 5. 9 5. 8 6. 0 6. 3 7. 5 8. 4 Gas Consumed vs Speed 10 9 Gas (L/100 km) 8 7 6 5 4 3 2 1 0 0 20 40 60 80 Speed (km/h) 100 120 140
Example � We can see the general shape of a parabola here, but it’s not perfect � Why? Because these is modeling a real-life situation with real data, not perfect data Gas Consumed vs Speed 10 9 Gas (L/100 km) 8 7 6 5 4 3 2 1 0 0 20 40 60 80 Speed (km/h) 100 120 140
Example � The curve that models this data is: � y = 0. 0009(x – 75)2 + 5. 8 � Not pretty, but it’s accurate and realistic Gas Consumed vs Speed 10 9 Gas (L/100 km) 8 7 6 5 4 3 2 1 0 0 20 40 60 80 Speed (km/h) 100 120 140
In Summary… � If you know the coordinates of the vertex (h, k) and one other point on a parabola, you can determine the equation of the relation using y = a(x – h)2 + k
