12 Quadratic Functions

Linear Slope-Intercept Form

Manipulate[
equation=Style["y = "<>ToString[b]<>" + "<>ToString[m]<>"x",Bold,12];
Plot[b+m x,{x,-5,5},PlotRange->{-5,5},PlotLabel->equation,PlotStyle->Red],
Style["\!\(\*Cell[TextData[Cell[BoxData[
FormBox[
RowBox[{"y", " ", "=", " ", 
RowBox[{"b", " ", "+", " ", 
RowBox[{"m", " ", "x"}]}]}], TraditionalForm]]]]]\)",Bold,14],{{b,1},-4,4},{{m,1},-10,10}]

Linear Point-Slope Form

Manipulate[
equation=Style["y = "<>ToString[m]<>"(x - "<>ToString[h]<>") + "<>ToString[k],Bold,12];
Plot[m (x-h)+k,{x,-5,5},PlotRange->{-5,5},PlotLabel->equation],
Style["\!\(\*Cell[TextData[Cell[BoxData[
FormBox[
RowBox[{"y", " ", "=", " ", 
RowBox[{
RowBox[{"m", " ", 
RowBox[{"(", 
RowBox[{"x", "-", "h"}], ")"}]}], "+", "k"}]}], TraditionalForm]]]]]\)",Bold,14],{{m,1},-10,10},{{h,0},-4,4},{{k,0},-4,4}]

Quadratic Standard Form

Manipulate[
equation=Style["y = "<>ToString[a]<>"(x^2) + "<>ToString[b]<>"x + "<>ToString[c],Bold,12];
Plot[a (x^2)+b x+c,{x,-5,5},PlotRange->{-5,5},PlotLabel->equation],
Style["\!\(\*Cell[TextData[Cell[BoxData[
FormBox[
RowBox[{"y", " ", "=", " ", 
RowBox[{
RowBox[{"a", " ", 
SuperscriptBox["x", "2"]}], " ", "+", " ", 
RowBox[{"b", " ", "x"}], " ", "+", " ", "c"}]}], TraditionalForm]]]]]\)",Bold,14],{{a,1},-2,2},{{b,0},-2,2},{{c,0},-2,2}]

Quadratic Factored Form

Manipulate[
equation=Style["y = "<>ToString[a]<>" (x - "<>ToString[r]<>") (x - "<>ToString[s]<>")",Bold,12];
Plot[a (x-r)(x-s),{x,-5,5},PlotRange->{-5,5},PlotLabel->equation],
Style["y = a (x - r) (x - s)",Bold,14],{{a,1},-2,2},{{r,0},-4,4},{{s,0},-4,4}]

Quadratic Vertex Form

Manipulate[
equation=Style["y = "<>ToString[a]<>"(x - "<>ToString[h]<>")^2 + "<>ToString[k],Bold,12];
Plot[a (((x-h))^2)+k,{x,-5,5},PlotRange->{-5,5},PlotLabel->equation],
Style["\!\(\*Cell[TextData[Cell[BoxData[
FormBox[
RowBox[{"y", " ", "=", " ", 
RowBox[{
RowBox[{"a", " ", 
SuperscriptBox[
RowBox[{"(", 
RowBox[{"x", " ", "-", " ", "h"}], ")"}], "2"]}], " ", "+", " ", "k"}]}], TraditionalForm]]]]]\)",Bold,14],{{a,1},-2,2},{{h,0},-4,4},{{k,0},-4,4}]