Plot Curves: Package pgfplots
Parabolas, $\mathcal{P}_{a,b,c}$
\[
y=ax^2+bx+c,
a \neq 0
\]
Vertex:
\[
\overrightarrow{OV}
=
\begin{pmatrix}x_0\\y_0\end{pmatrix}
=
\begin{pmatrix}
-\frac{b}{2a}
\\
-\frac{b^2-4ac}{4a}
\end{pmatrix}
=
\begin{pmatrix}
-\frac{b}{2a}
\\
-a\left( \frac{b}{2a} \right)^2
+c
\end{pmatrix}
\]
Observe:
\[
y_0
=
-a x_0^2+c,
\]
$V \in \mathcal{P}_{-a,0,c}=\mathcal{P}_V$.
@Image Fig.svg
@Code Fig.tikz.tex height=300px
@Image Fig.png