Identifying The Domain, Range and Horizontal Intercepts of a Quadratic Function
For each of the following quadratic functions:
  1. Determine the Domain of the Function
  2. Determine the Range of the Function
  3. Use the Intersect Feature and your graphing calculator to determine the Horizontal Intercepts, if any. Round your answers to one decimal places as needed

    [Hint: If two Horizontal Intercepts exist, enter them as (x1,y1),(x2,y2)\displaystyle {\left({x}_{{1}},{y}_{{1}}\right)},{\left({x}_{{2}},{y}_{{2}}\right)}. If only one exists, enter (x1,y1)\displaystyle {\left({x}_{{1}},{y}_{{1}}\right)}. If none exist, enter DNE\displaystyle {D}{N}{E}]
FunctionDomain
In Interval Notation		Range
In Interval Notation		Horizontal Intercepts
As a list of ordered pairs
f(x)=3x2+6x−6\displaystyle {f{{\left({x}\right)}}}={3}{x}^{{2}}+{6}{x}-{6}
 
 
g(x)=x2−4x+6\displaystyle {g{{\left({x}\right)}}}={x}^{{2}}-{4}{x}+{6}
 
 
f(x)=−x2+8\displaystyle {f{{\left({x}\right)}}}=-{x}^{{2}}+{8}
 
 
p(t)=3t2+12t\displaystyle {p}{\left({t}\right)}={3}{t}^{{2}}+{12}{t}
 
 
h(x)=2x2\displaystyle {h}{\left({x}\right)}={2}{x}^{{2}}
 
 

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