Thread: Linear Quadratic System

Determine the restrictions on the y-intercept so that intersects with a line with slope 2 in more then one place

let k = y-intercept for the line

points of intersection can be found by setting the linear and quadratic equations equal to each other ...



set the equation equal to 0 ...



if the line intersects the parabola twice, then the above quadratic must have two distinct real roots.

for the quadratic to have two distinct real roots, the discriminant,



solve the inequality for k.