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The given function is `y = x^2 - 2x - 5.`
This is the equation of a parabola in its standard form.
To find its vertex transform the given function into the equation of the parabola in its vertex form i.e `y=a(x-h)^2+k` where `(h,k)` is its vertex.
So, `y = x^2 - 2x - 5`
`rArr y = x^2 - 2x +1-1- 5`
Here, `h=1` , `k=-6`
a) Hence, the vertex of the given function is (1,-6).
To find the x intercepts set `y=0` and solve. So,
`x^2 - 2x - 5=0`
Applying the quadratic formula we get:
b) Therefore, the x intercepts are `1+sqrt6` and `1-sqrt6` .
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