Question

Set up an equation of a tangent to the graph of the following function.
$y=x^2-2x+5$ at the point of its intersection with the y axis.

Answer 1

$y=x^2-2x+5$

The point of intersection at y-axis has abscissa as 0

$y=0^2-2\left(0\right)+5=5$

The point of intersection with y-axis is (0,5)

$\frac{dy}{dx}=2x-2$

${\left(\frac{dy}{dx}\right)}_{x=0}=-2=m$

$m(x-x_1)=y-y_1$

$-2(x-0)=y-5$

$2x+y-5=0$