Identifying The Characteristics of Quadratic Functions
For each of the following quadratic functions (Show your work):
  1. Calculate the vertex by hand and write it as an ordered pair.
  2. Determine the axis of symmetry and write it as a linear equation (x = # or t = #).
Function−b2a\displaystyle \frac{{-{b}}}{{{2}{a}}}f(−b2a)\displaystyle {f{{\left(\frac{{-{b}}}{{{2}{a}}}\right)}}}VertexAxis of Symmetry
(Be sure to use the proper variable)
g(x)=x22−6x+8\displaystyle {g{{\left({x}\right)}}}=\frac{{x}^{{2}}}{{2}}-{6}{x}+{8}
 
f(x)=6x2+12x+4\displaystyle {f{{\left({x}\right)}}}={6}{x}^{{2}}+{12}{x}+{4}
 
h(t)=4t2\displaystyle {h}{\left({t}\right)}={4}{t}^{{2}}
 
f(x)=−x2+1\displaystyle {f{{\left({x}\right)}}}=-{x}^{{2}}+{1}
 
p(t)=5t2+20t\displaystyle {p}{\left({t}\right)}={5}{t}^{{2}}+{20}{t}
 

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