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

May 19, 2017

$y = {\left(x + 0\right)}^{2} - 1$

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: $y = {x}^{2} + 0 x - 1$

$y = {\left(x + \frac{0}{2}\right)}^{2} + k - 1$

$k + {\left(\frac{0}{2}\right)}^{2} = 0 \implies k = 0$

Thus we have:

$y = {\left(x + 0\right)}^{2} - 1$

Thus the vertex is at $\left(0 , - 1\right)$
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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.