Systems with Nonlinear Equations

A quadratic-linear system pairs a parabola with a line: [formula] Graphically, you're finding where the line intersects the parabola. There can be: - 2 intersections (line cuts through parabola) - 1 intersection (line is tangent to parabola) - 0 intersections (line misses parabola) Solving: substitute the linear equation into the quadratic (or set them equal).

Since both equations equal y, set them equal: [formula] Rearrange to standard form and solve the resulting quadratic.

Example: Solve: y = x^2 and y = x + 2