I've been stuck on some math work and I'm not sure how to do it. It involves finding the point where a quadratic and linear function intersect only once.
Determine the value of $k$ such that $g(x) = 3x+k$ intersects the quadratic function $f(x) = 2x^2 -5x +3$ at exactly one point.
How do I figure out the $k$ value?
Set the two RHS's equal to each other: $3x +k = 2x^2 - 5x+3$.
Rearrange: $2x^2 - 8x +(3-k) = 0.$
There is precisely one intersection if and only if the descriminant of this quadratic equals zero.
The descriminant is $64 -8(3-k) = 40 + 8k $, and this equals zero if and only if $k=-5$.