Hello, this is the first time I have ever asked for homework help here. Please, help.

I need to find the lowest slope of a line in order for it to intersect with a parabola.

If the parabola is, say, 2x^2+5, how would I determine the lowest slope of the line that intersects with it?

A line can intersect with the parabola at any slope depending on its X and Y intercepts.

Can you provide a diagram?

I don't have the software at the moment, but I will try to explain it more clearly.

The parabola is concave up, with the origin a certain number above (y) the origin, but the x value of the origin is 0.

The line intersects the origin. I want to determine the value of the slope which will intersect the parabola only once, on the right side of the origin (this will presumably be the lowest slope).

It sure sounds to me like the line you want is y = 5, where the slope is zero.

It would be nice, certainly, but the line must intersect the origin.

....

I want to find the slope of that line. Thanks for your help, by the way.

take the derivative of the parabola with respect to x and plug in your y value to rearange it into a y=mx+b format. what you are looking for is called a tangent line.

Kanchi is exactly right.

Plug in which Y value?

y=2x^2+5
y'=4x

Then?

The slope must be 4x where x is the intersection between the parabola and the tangent line. You need to find the value for x where the tangent line intersects the origin.

Ignore me.

Got it, thanks all.