Question

Compare the graphs of y = 2x² + 8x + 8 and y=x² without graphing the functions. How can factoring help in comparing the parabolas? Explain in detail.

Answer 1

$$y=2x^2+8x+8=2(x^2+4x+4)=2(x+2)^2$$

$$f(x)=x^2$$

Shift the graph to the left 2 units

$$f(x+2)=(x+2)^2$$

Stretch vertically by 2

$$2f(x+2)=2(x+2)^2$$

We can ontain the graph of $y=2x^2+8x+8$ from the graph of $y=x^2$ using the Graph Transformations.