Explore how rewriting a quadratic expression reveals key features of its graph.
[i]Answer these open ended questions on your own or with others to form deeper math connections.[/i]
What can you tell about the graph of [math]f[/math] given its equation [math]f\left(x\right)=x^2+8x+2[/math]? What else can you tell about the graph if the equation is rewritten as [math]f\left(x\right)=\left(x+4\right)^2-14[/math]?
What are some characteristics you can interpret about any quadratic function that is written in the form [math]f\left(x\right)=a\left(x-h\right)^2+k[/math]?
How does the process of completing the square help you gather information about the graph of a quadratic function?