# Quadratics

### Factored Form

## Summary of the Unit

- Types of Factoring:
- Greatest Common Factor
- Simple factoring (a=1)
- Complex factoring
- Special case - Difference of squares
- Special case – Perfect square

- x- intercepts can be found by solving for x in the factor and once there are 2 x-intercepts we can find the average of both and figure out the axis of symmetry.

- After the axis of symmetry is found, that value of x will be substituted into the original equation to solve for y.

- That is how we figure out the vertex, it is the value of y and the AOS.

- Once the 2 x intercepts are plotted and so is the vertex then that is the completed 3 point method

## https://www.youtube.com/watch?v=ChB5Ox7MbkQ

## Word problem

a)What is the initial height of the toy rocket?

b)When will the rocket hit the ground

c) What was the maximum height?

d) How long does it take the rocket to reach its maximum height?

## answers

b) The rocket hits the ground at 7 seconds.

-t^2+4t+21

-(t^2-4t-21)

-7,3

-(t^2 + 3t)-(7t-21)

-[t(t+3)-7(t+3)]

(t-7)(t+3)

t-7=0

t=7

t+3=0

t=-3

c) The maximum height is 25 meters.

AOS= 7-3/2 = x=2

sub x into original equation.

-t+4t+21

-2^2+4(2)+21

-4+8+21

y = 25 meters

d) It takes the rocket 2 seconds.

AOS=2