Write the equation of a linear graph that doesnt have any points of intersection with the curve with equation y=x^2+2x

Question

Help would be appreciated with the following question: I can probably imagine where it would go and write something totally away but what would be a mathematical way to do this and a proof of answer. Write the equation of a linear graph that doesn't have any points of intersection with the curve with equation y=x^2+2x

Answer 1

Here's a hint. A line ("linear graph") will have the form $y = mx + c$

If there were an intersection with $x$ coordinate $X$, at that point, you'll have equality between the two functions, i.e. $X^2 + 2X = mX + c$

That's a quadratic equation. Can you think of what condition must hold for no such intersection to exist (and remember, when discussing graphical intersections at an elementary level, we're always talking about real numbers)?

Can you finish?