Nonlinear systems

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   Consider the system $y = x^{2} + 3x + 4$ and $y = x^{2} - 3x - 32$. Find the $x$-coordinate of the single point where the two parabolas intersect.

2. Warm-up

   Consider the system $y = x^{2} + 3x + 5$ and $y = x^{2} + 2x + 1$. Find the $x$-coordinate of the single point where the two parabolas intersect.

3. Warm-up

   Consider the system $y = x^{2} - 4x - 3$ and $y = x^{2} - 3x - 9$. Find the $x$-coordinate of the single point where the two parabolas intersect.

Problems shown under their original terms: Generated (template, solver-computed).