Question

How do you write the Vertex form equation of the parabola `y=x^2-1`?

Answer 1

`y=(x+0)^2-1`

Explanation:

The Vertex form is derived by the process called 'completing the square'.

Assumption: You do not need a step by step explanation.
If you do then see the example: https://socratic.org/s/aEP7wZdu

Using a place holder write as: `y=x^2+0x-1`

`y=(x+0/2)^2+k-1`

`k+(0/2)^2=0 =>k=0`

Thus we have:

`y=(x+0)^2-1`

Thus the vertex is at `(0,-1)`
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This is as expected because we have lowered by 1 the standard graph of `y=x^2`. The axis of symmetry for `y=x^2` is the y-axis.