Question

How do you write the function in standard form `y=-(x+3)(x-4)`?

Answer 1

`-x^2+x+12`

Explanation:

We must ensure that each term in the 2nd bracket is multiplied by each term in the 1st bracket.
This can be done as follows. Leaving the - outside the brackets until after multiplication.

`(color(red)(x+3))(x-4)=color(red)(x)(x-4)color(red)(+3)(x-4)`

now distribute the brackets and collect like terms.

`=x^2-4x+3x-12=x^2-x-12`

now go back and do multiplication by - 1

`rArr-(x^2-x-12)=-x^2+x+12`