Quadratics

Factored Form

Learning goals

  • I should be able to factor simple trinomials, complex trinomials, difference of squares and perfect squares
  • I should be able to find the x-intercepts of a factor
  • I should be able to find the vertex and graph using the 3-point method

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

Factored Form - Difference of Squares and Perfect Squares

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

Word problem

The height, h, in meters, of a toy rocket at any time, t, in seconds, during its flight can be estimated using the formula h= -t^2+4t+21.

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

a) The initial height of the toy rocket is 21 meters.

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