What is the equation of a parabola that touches the x-axis at (4, 0) and the y-axis at (0, 6)

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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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