Emerson Barnes

2022-01-21

What are the coordinates of the vertex of
$y={x}^{2}-4x-5$?

helsinka04

Expert

Step 1
$y={x}^{2}-4x-5$
is a parabola with a slope (for arbitrary values of x) given by the expression
$\frac{dy}{dx}=2x-4$
This slope is equal to 0 at the vertex of the parabola
$2x-4=0$
$\to x=2$
When $x=2$ the equation for the parabola gives us
$y={\left(2\right)}^{2}-4×\left(2\right)-5$
$=-9$
So the coordinates of the vertex of the parabola are

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