The vertex form of a quadratic is given by y = a(x – h)2 + k, where (h, k) is the vertex.

In our case (h, k) = (-9.-16) thus y = a(x - (-9))^2 + (-16) or

y = a(x + 9)^2 -16

We find a using the fact that for x = 0, y = - 70

a(0 + 9)^2 -16 = -70

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click here to see the equation solved for a

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a = -54/81

a = -2/3

Now we can write the vertex form: y = (-2/3)(x + 9)^2 -16

The standard forms is y=ax^2+bx+c or in our case:

y = (-2/3)(x + 9)^2 -16

y = (-2/3)(x^2 + 18x + 81) - 16

y = (-2/3)x^2 - 12x - 54 - 16

y = (-2/3)x^2 - 12x - 70

The parabolic function y = (-2/3)x^2 - 12x - 70 has maximum (since -2/3 <0) equal to:

y max = c - b^2/4a, where a = -2/3, b = -12, c = -70

y max = -70 - (-12)^2/(4*(-2/3))

y max = -16

We find the symmetric point by finding the nonzero solution of the equation:

(-2/3)x^2 - 12x - 70 = -70

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click here to see the equation solved for x

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x = -18

The symmetric point is (-18, -70).