Given $f(x)=x^2-4x+3$, find the points on the curve $y=f(x)$ where the tangent to the curve passes through -6.

Question

Given $f(x)=x^2-4x+3$, find the points on the curve $y=f(x)$ where the tangent to the curve passes through $(0,-6)$. State the equations of the tangents at these points.

Hi everyone, I tried to find the points on curve but I'm stuck. I used the formula $y-y_1=m(x-x_1)$ but I couldn't get an answer. Can anyone help me with this? Thanks.

Answer 1

HINT:

The equation of any straight line passing through $(0,-6),$

is $$\dfrac{y+6}{x-0}=m$$ where $m$ is the gradient

Now find the abscissa of the intersection(s) by replacing $y$ with $mx-6$

For tangency, the intersections must converge