QUADRATIC RELATIONSHIPS
Unit 2: Factored Form
Learning Goals
- I will be able to factor using distributive property and finding the common factor.
- I will be able to factor both simple and complex trinomials.
- I will be able to factor perfect square trinomials and difference of squares.
Summary Of Unit
Factored form: y= a(x-r) (x-s)
- the value of "a" gives you the shape and direction of opening
- the value of r and s give you the x-intercepts
- to find the y-intercept, set x=0 and solve for y
- Solve using the factors
- Types of Factoring:
- Common Factoring- finding the GCF of numbers to factor. Ex: 4x^2 + 8x
- Factor By grouping- factored by grouping terms that do have a common factor.
- Simple Trinomial- factoring when the A value is 1 Ex: x^2 -3 -4
- Complex Trinomial- factoring when the value of a is higher than 1 Ex: 8x^2 + 25x + 4
- Difference of squares- Ex: x^2 + 64
- Perfect square- In a perfect square trinomial, the first and last terms are perfect squares, and the middle term is twice the product of the square roots of the first and last terms.
- Ex: x^2 +6x +9
- EXPAND THE FACTORS to see if the answer equals to the first equation
- Left Side VS Right Side
Word Problem Using Factored Form
The height of a rock thrown can be approximated by the formula h= -5t^2 + 15t + 20 , where “t” is the time in seconds, and “h” is the height, in metres
a) When does the rock hit the ground?
To do this question we need to set H to zero.
This is how it should look like:
-5t^2 + 15t +20= 0
Next, I am going to take the common out and divide everything inside by -5:
-5 (t^2 -3t- 4) = 0
In the bracket we can see that it is a simple trinomial. So I am going to factor it and complete all the steps to finding when the rock hits the ground.
-5 (t^2 -3t- 4) = 0
-5(t-4) (t+1) = 0
t-4= 0 t+1=0
t= 4 t=-1
Therefore, it will take the rock 4 seconds to hit the ground.
b) What is the maximum height the rock reaches, and when does it reach its maximum height?
AOS= 4 + (-1)/ 2= 1.5
Maximum Height: -5(1.5)^2 + 15(1.5) + 20
=31.25 m
Vertex= (1.5, 31.25)
Therefore, the rock reaches the maximum height of 31.25m at 1.5 seconds.
Video Of Factoring
FACTORED FORM