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**mr fantastic** a) The (minimum) turning point is at (4, 6). You're familiar with the turning point form of a parabola - $\displaystyle y = a(x - h)^2 + k$ where the turning point is at (h, k) - right?

So *any* answer of the form $\displaystyle y = a(x-4)^2 + 6, \, a > 0, \,$ satisfies the given property. The book chose a = 3. Other concrete answers can be got by choosing a = 1, 2, 4, 1/2, ......

b) The turning point has y-coordinate y = 7. So k = 7 in the turning point form. In the turning point form, a 'controls the shape', so a = 3.

So *any* answer of the form $\displaystyle y = 3(x - h)^2 + 7 \,$ satisfies the given properties. The book chose h = 0, probably the simplest answer. Other concrete answers can be got by choosing h = 1, 2, 3, -1, -2 -3, 1/2, -1/2, ......