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Find analytical expression of a parabola from its graph transformation

Question:

Move the parabola y = - (1/3) x2 to the left by 2 units and then down 1 unit. What is the analytical expression of the resulting parabola?

Solution:

The graph shows the parabola y = - (1/3) x2

how to find analytical expression of a parabola from its graph transformation?

When move the graph y = - (1/3) x2 left by 2 units, the resulting parabola is y = - (1/3) (x + 2)2, then move the graph down 1 unit, the resulting parabola is y = - (1/3) (x + 2)2 - 1

how to find analytical expression of a parabola from its graph transformation?

Look the figure above, the blue curve is the parabola y = - (1/3) x2. When move the blue curve left by 2 units, the resulting parabola is y = - (1/3) (x + 2)2 which is orange curve. When move the orange curve down 1 unit, the resulting parabola is y = - (1/3) (x + 2)2 - 1 which is grey curve. Watch the video for more details.