Question

Describe the translations applied to the graph of y 5 x2 to obtain a K graph of each quadratic function. Sketch the graph.

y=(x+1)^2-2

Answer 1

First, we can compress the initial function $y=5x^2$ along y-axis. We get

$$y=x^2.$$

Then we can shift the function by 2 units down y-axis:

$$y=x^2-2.$$

Then we shift the function left 1 unit and here is what we get:

$$y=(x+1)^2-2.$$

In graph below, red is the initial function, purple is the final function: