Question

How do you write y=2(x-1)^2-3 in standard form?

Answer 1

`2x^2-4x-1`

Explanation:

`"the equation of a parabola in standard form is"`

`•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0`

`"expand "(x-1)^2" and collect like terms"`

`y=2(x^2-2x+1)-3`

`color(white)(y)=2x^2-4x+2-3`

`color(white)(y)=2x^2-4x-1larrcolor(blue)"in standard form"`

Answer 2

Standard form:
`y=2x^2-4x-1`

Explanation:

`y=2(x-1)^2-3`

We can start by expanding `(x-1)^2`

`(x-1)(x-1)`

=

`x^2-2x+1`

Now we have:

`y=2(x^2-2x+1)-3`

To get the x^2-2x+1 out of the parentheses we multiply the expression by 2 then subtract by 3:

`y=2(x^2-2x+1)-3`

=

`y=(2x^2-4x+2)-3`

=

`y=2x^2-4x-1`

This is in standard form:

`y=2x^2-4x-1`