We will derive this by completing the square.
General Form:
$f(x)=ax^2+bx+c$
Factor out $a$:
$f(x)=a \Bigl(x^2+$
$x+$
$\Bigl)$
Add and subtract the term needed to complete the square:
$f(x)=a \Bigl(x^2+\frac{b}{a}+$
$+\frac{c}{a}-$
$\Bigl)$
Complete the square:
$f(x)=a \Bigl\{\bigl(x+$
$\bigr)^2+\frac{c}{a}-\frac{b^2}{4a^2}\Bigr\}$
Combine into a single fraction:
$f(x)=a \Bigl\{\left(x+\frac{b}{2a}\right)^2+$
$\Bigr\}$
Factorize a negative:
$f(x)=a \left\{\left(x+\frac{b}{2a}\right)^2-\frac{b^2-4ac}{4a^2}\right\}$
Distribute $a$:
$f(x)=a \left(x+\frac{b}{2a}\right)^2-$
The equation of the axis of symmetry is $x=$
To find the $x$-intercepts, we let $f(x)=$
and solve for $x$.
This will be done on the worksheet.