1. ## Shape of graph of quadratic functions

if the line x-y=4k+2 does not meet the curve y=k(x+1)(x-3), find the range of values of k.

2. Originally Posted by mastermin346
if the line x-y=4k+2 does not meet the curve y=k(x+1)(x-3), find the range of values of k.

First note that the first equation can be written as

$\displaystyle y = x - 4k - 2$.

Now, if the two equations do not intersect, then you have to solve

$\displaystyle x - 4k - 2 \neq k(x + 1)(x - 3)$ for $\displaystyle k$.

3. In other words try to solve x- 4k- 2= k(x+1)(x-3). For what values of k does that quadratic equation not have a solution?

4. Originally Posted by HallsofIvy
In other words try to solve x- 4k- 2= k(x+1)(x-3). For what values of k does that quadratic equation not have a solution?
If you need another hint: rearrange the above equation to form a quadratic of the form $\displaystyle ax^2 - bx + c = 0$.

For there to be no solution, the discriminant must be less than 0. That is, you are looking for the values of k such that $\displaystyle \Delta = b^2 - 4ac < 0$