# Vertical Shifts of Quadratic Functions

Vertical shifts of quadratic functions involve transformations that alter the position of the graph along the y-axis while maintaining its basic shape. These shifts occur when constants are added or subtracted to the function, affecting the vertex and the position of the parabola. Understanding vertical shifts is crucial in analyzing quadratic equations, as they indicate changes in the graph's position relative to the coordinate plane. By mastering this concept, mathematicians and scientists can accurately model various phenomena, from projectile motion to financial trends, by adjusting the function's parameters to reflect real-world scenarios.

Questions

- How do you sketch the graph of #y=(-x)^2# and describe the transformation?
- How do you sketch the graph of #y=x^2+0.5# and describe the transformation?
- How do you sketch the graph of #y=(x+3)^2+6# and describe the transformation?
- How do you sketch the graph of #y=(x+6)^2-2# and describe the transformation?
- How do you sketch the graph of #y=x^2-10# and describe the transformation?
- How do you sketch the graph of #y=-(x+2)^2+2 and describe the transformation?
- How do you sketch the graph of #y=x^2-5# and describe the transformation?
- How do you sketch the graph of #y=-x^2+2# and describe the transformation?
- How do you sketch the graph of #y=2(x+4)^2-3# and describe the transformation?
- How do you sketch the graph of #y=(x+3)^2# and describe the transformation?
- How do you sketch the graph of #y=-3x^2# and describe the transformation?
- How do you sketch the graph of #y=(x-4)^2# and describe the transformation?
- How do you sketch the graph of #y=x^2-2x# and describe the transformation?
- How do you sketch the graph of #y=(x-3)^2# and describe the transformation?
- How do you sketch the graph of #y=-5x^2# and describe the transformation?
- How do you sketch the graph of #y=2x^2-3# and describe the transformation?
- Where do you start when you are trying to graph quadratic functions?
- What transformation transforms (a, b) to (a, −b)?
- How do you sketch the graph of #y=x^2+8# and describe the transformation?
- How do you sketch the graph of #y=(x+3)^2# and describe the transformation?