Question

How do you write the function in standard form `y=2(x-1)(x-6)`?

Answer 1

`y=2x^2-14x+12`

Explanation:

Standard form of a quadratic takes the shape `ax^2+bx+c=0`. This usually comes about from an expansion of the expression `(alphax+beta)(gammax+delta)`, using the distributive property such that `(a+b)(c+d)=ac+ad+bc+bd`.

Using these rules, we now expand the expression
`y=(2)(x-1)(x-6)` by first multiplying the first two brackets, to get
`y=( 2*x + 2*-1)(x-6) = (2x-2)(x-6)`. Next we expand the last two brackets, to get
`y=2x*x+2x*(-6)+(-2)* x+(-2)*(-6)` `= 2x^2-12x-2x+12`
Lastly we simplify by grouping like terms, to get
`y=2x^2-14x+12`, the answer.

I hope that helped!