Find a function whose graph is a parabola with vertex (4,9) and that passes through the point (5,12). How do you find this function??

Tuesday, February 7, 2012

We will write
the function in the vertex form:

$\displaystyle{f{{\left({x}\right)}}}={a}{{\left({x}-{h}\right)}}^{{2}}+{k}$ such that (h,k) is the
vertex.

$\displaystyle==\gt{f{{\left({x}\right)}}}={a}{\left({x}-{4}\right)}+{9}$

Now given the point
(5,12) passes through the line.

$\displaystyle==\gt{f{{\left({5}\right)}}}={12}$

$\displaystyle==\gt$
f(5)= a(5-4)^2 +9 = 12

$\displaystyle==\gt{a}+{9}={12}$

$\displaystyle==\gt{a}={12}-{9}=$
3

$\displaystyle==\gt{f{{\left({x}\right)}}}={3}{{\left({x}-{4}\right)}}^{{2}}+{9}$

$\displaystyle==\gt{f{{\left({x}\right)}}}={3}{\left({{x}}^{{2}}-{8}{x}+{16}\right)}+$
9

== $\displaystyle\gt{f{{\left({x}\right)}}}={3}{{x}}^{{2}}-{24}{x}+{57}.$

Spooky Notes