For week 9 of precalculus 11, we did the last 3 lessons of unit 4. (4.5, 4.6, 4.7)

4.5, and 4.6 focused on converting equations from one form to another between general, standard, and factored form in order to find all the information necessary to graph an equation.

For Example, and equation of the form y = x^{2 } + 6x + 8, we already know the y-intercept as “c” (+8), and can be converted into vertex (standard) form by completing the square.

= y = (x^{2 } + 6x + 9) – 9 + 8

= y = (x + 3)^{2 } – 1

The vertex can now be found as (-3, -1).

and the equation can also be factored.

y = (x + 2)(x + 4) and we now know the x intercepts which is all the information to make a graph.

Finally, lesson 4.7 focused on using these strategies to solve word problems involving quadratics, such as revenue, maximum lengths, etc…