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The parabola to be determined touches the x-axis at (4, 0) and the y-axis at (0, 6). There are two possible parabolas that can meet this condition, one opens upwards and the other opens to the left.
The general equation of a parabola is y = ax^2 + bx + c. The parabola touches the x-axis at (4, 0)
=> 0 = a*16 + 4b + c ...(1)
It touches the y-axis at (0, 6)
=> 6 = 0 + 0 + c
Substitute c = 6 in (1)
=> 16*a + 4b + 6 = 0
It is not possible to determine unique values for a and b from this equation. As seen in the graph below, there are an unlimited number of parabolas that meet the given conditions.
There is no unique parabola that passes through the given points.
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