Systems with a Curve Worksheet with Answer Key

What's on the worksheet

1. Solve each system by substitution, check every point, or say the graphs do not meet.
   \begin{cases} y = x^2 + 3x - 2 \\ y = 2x + 4 \end{cases}\begin{cases} y = -x^2 + 4x \\ y = x - 4 \end{cases}\begin{cases} y = 2x^2 - 5x + 1 \\ y = 3x - 7 \end{cases}\begin{cases} y = 3x^2 - 2x \\ y = 4x + 9 \end{cases}\begin{cases} y = x^2 - 4x + 2 \\ 2x - y = 6 \end{cases}
2. Say how many points each pair of graphs shares without solving.
   \begin{cases} y = x^2 + 5x + 1 \\ y = x - 3 \end{cases}\begin{cases} y = -2x^2 + x \\ y = 3x + 1 \end{cases}\begin{cases} y = x^2 - 3x \\ y = 2x - 5 \end{cases}\begin{cases} y = 3x^2 - x + 2 \\ x + y = 2 \end{cases}\begin{cases} y = -x^2 + 4 \\ y = 3 \end{cases}
3. Solve a parabola and line system and give each point exactly.
4. Solve a system of two parabolas and explain why they cannot share two points.
5. Show how the line y equals 2x plus k meets the parabola for different values of k.
6. Find the error in how a student wrote the solutions of a system.
7. Summer camp catapult: find where the water balloon lands on the hill.