Thread: Finding value to make two graphs tangent

Find a negative value of k so that the graph of y = x2 - 2x + 7 and the graph of y = kx + 5 are tangent?

It says the answer is -2-2sqt2

I graphed this and it didn't look tangent to me. Thanks.

It does look tangent.

Hint: consider the difference of the two functions and find when it has a single root.

I am putting it in the calculator wrongly. When I evalued K and then put it in the calculator, it looked tangent.

This is how I am putting it in: "(-2-2sqt2)x+5"

Originally Posted by benny92000

I am putting it in the calculator wrongly. When I evalued K and then put it in the calculator, it looked tangent.

This is how I am putting it in: "(-2-2sqt2)x+5"

You need the line and the parabola to intersect at a single point. Therefore you need the discriminant of to equal zero ....

Ok so I got x^(2) (-2-k)x + 2 = 0

Ultimately I got k^(2) +4k -4 = 0 I used quadratic formula and came up with the correct answer. So theoretically, when you subtract the two equations, the solution(s) of that equation is the intersection(s) of both equations? And with resepect to the calculator, did I plug it on wrongly? Why did they not appear to intersect?

Originally Posted by benny92000

So theoretically, when you subtract the two equations, the solution(s) of that equation is the intersection(s) of both equations?

I would be careful with terminology. First, one can only talk about the intersection of graphs (which are geometrical figures), not equations. Second, we can draw all points satisfying two equations and , but this would not be the set of points satisfying . For example, points satisfying 2x + 3y = 0 and x + y = 0 are lines that intersect at just one point (0, 0), but points satisfying x + 2y = 0 fill a whole line. What we have in the original problem are equations and , to be sure, but not arbitrary equations. Rather, they are definitions of functions with only y in the left-hand side.

So, the correct statement is, If you have functions and , then the solutions of the equation give the (x-coordinates of the) intersection points of the graphs of the two functions.

Originally Posted by benny92000

And with resepect to the calculator, did I plug it on wrongly? Why did they not appear to intersect?

I don't have a graphing calculator, so I am not sure. There are many possible reasons. E.g., you may need to adjust the window size, write "2*sqt(2)" instead of "2sqt2," etc. Try using 1.41 instead of sqt2.