1. The problem asks to draw the graphs of three functions: a. $y=(x-1)^2+2$ b. $y=(x-2)^2-3$ c. $y=(x+1)^2+1$ 2. Each function is a quadratic in vertex form $y=(x-h)^2+k$, where $(h,k)$ is the vertex. 3. For function a: $y=(x-1)^2+2$ - Vertex is at $(1,2)$ - The parabola opens upwards because the coefficient of the squared term is positive. 4. For function b: $y=(x-2)^2-3$ - Vertex is at $(2,-3)$ - The parabola opens upwards. 5. For function c: $y=(x+1)^2+1$ - Vertex is at $(-1,1)$ - The parabola opens upwards. 6. These are all standard parabolas shifted horizontally and vertically according to their vertices. Final answer: - Graphs of the three parabolas with vertices at $(1,2)$, $(2,-3)$, and $(-1,1)$ respectively, all opening upwards.