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**Bushy** **Consider the function** $\displaystyle f(x)= x^2+k, k\in \mathbb{R}$** and the tangent to the curve at **$\displaystyle x=a$

**Show that the tangent does not pass through the origin if **$\displaystyle k<0$ .

It seems obvious that it does that it pass through the origin when I draw the function for $\displaystyle k<0$ as the origin is 'inside' the parabola. But is this argument enough?

I also have the equation of the tangent being $\displaystyle \displaystyle y = f'(a)x+c \implies y = 2ax+c$