Help with quadratic functions?

Question

y = ax^2+bx+c
y = -1/6x-x-3

y = a(x-h)^2+k
y = -1/6(x+1/4)^2+3/4

Are the equations equivalent to one another?

Answer 1

No, if you substitute 0 for x, the first equation equals -3 and the second equation equals 71/96. These are not equivalent.


If we work out the second equation:
y = -1/6(x+1/4)^2+3/4
y = -1/6(x² + ½x + 1/16) + 3/4
y = -1/6x² -1/12x - 1/96 + 3/4
y = -1/6x² -1/12x + 71/96

This is clearly different from the first equation.

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Answer 2

Yes, if by equivalent you mean are they both quadratic equations and are in the same general form.