how to form the quadratic function into y=ax^2+bx+c ?
$$\begin{array}{rcl}
y&=&
ax^2+bx+c\\\\
y&=&
a\left(
x^2+{b\over a}x\right)
+c\\\\
y&=&
a\left(
x^2+{b\over a}x \textcolor[rgb]{1,0,0}{
+ ({b\over 2a})^2 - ({b\over 2a})^2 }
\right)
+c\\\\
y&=&
a\left[(x+{b\over 2a})^2 - ({b\over 2a})^2
\right]
+c\\\\
y&=&a (x+{b\over 2a})^2 - {b^2\over 4a}+c\\\\
y&=&a (x+{b\over 2a})^2 + c - {b^2\over 4a}
\end{array}$$
how to form the quadratic function into y=ax^2+bx+c ?
$$\begin{array}{rcl}
y&=&
ax^2+bx+c\\\\
y&=&
a\left(
x^2+{b\over a}x\right)
+c\\\\
y&=&
a\left(
x^2+{b\over a}x \textcolor[rgb]{1,0,0}{
+ ({b\over 2a})^2 - ({b\over 2a})^2 }
\right)
+c\\\\
y&=&
a\left[(x+{b\over 2a})^2 - ({b\over 2a})^2
\right]
+c\\\\
y&=&a (x+{b\over 2a})^2 - {b^2\over 4a}+c\\\\
y&=&a (x+{b\over 2a})^2 + c - {b^2\over 4a}
\end{array}$$