# Week 9 Precalc 11

This week in Precalc 11 we finished unit 4 and started to review for the midterm neat the end of the week.

In lesson 4.6 we discovered Equivalent Quadratic equations.  When you can change functions to different forms such as vertex form, general form and factored form.

General form to standard form = complete the square

factored form to general form = FOIL

general form to factor form = factor

vertex form to general form = expand and simplify

In lesson 4.7 we learned about modelling problems with quadratic equations.  this was the hardest lesson of them all since it was all word problems and you have to be careful of what the question is asking for.

Ex :

Two numbers have a difference of 18.  the sum of their squares is a minimum.  determine the numbers.

$a-b=18$

\$latex.a^2+b^2=minimum\$

$a=18+b$

$(18+b)^2+b^2$

$2b^2+36b+324$

$2(b+9)^2-162+324$

$2(b+9)^2+162$

$b=a+18$

$b=-9+18$

$b= 9$

the numbers are -9 and 9.