Quadratics
Grade 10 Math
Shiyana Veerasingam
Factored Form
Factored form is writen in the form of y=a(x-r)(x-s). In factored form, it is given that you could find your x-intercepts for graphing.
Factoring is the process of mutiplying the variables in a standard equation to produce a simplified form. When you have a factored equation, you may begin to graph your cordinates (x-intercepts).
When given an equation in stadard form (ax^2+bx+c), in order to factor this, you must find two numbers that mutiply to equal c and those same two numbers must add up to equal bx.
Factored Form to Standard Form
This is the process in which you expand the brackets using the FOIL method. For example (x+3)(x+2) would look like x2+5x+6 when expanded correctly.
Outllined below are steps for the FOIL method:
x2--> x mutiplied by another x would equal x2
5x--> x mutiplied by 2 equals 2x
3 mutiplied by x equals 3x
when like terms are collected it equals 5x
6--> 3 mutiplied by 2 equals 6
Factored Form to Vertex Form
When converting Factored Form to Vertex Form the first step is to find the x intercepts by making y=0.
When found the x intercepts, the second step would be to find the axis of symmetry by adding the two x intercepts and dividing it by two.
The axis of symmetry would then be your x value, so the third step would be to plug that into your original equation and get the y value
Finding the Vertex
When given an equation in Factored Form, the first step would be to epand the brackets.
(x-2)(x-4)
x2-6x+8
The second step would be to take your bx value and divide it by two and then square it
(6/2)2 =9
The third step would be to cancel out what you just added to the equation so it doesnt effect anything
(x2-6x+9)-9+8
The fourth step would be to colloect like terms
(x2-6x+9) -1
The fifth step would be to factor
(x-3)2-1