Question

How do you write the quadratic function in standard form `y=4(x-1)^2+5`?

Answer 1

`y=4x^2-8x+6`

Explanation:

`y=4(x-1)^2+5` This is Vertex form.

Expand & simplify
`y=4\cdot(x-1)(x-1)+5`
`y=4\cdot(x^2-2x+1)+5`
`y=4x^2-8x+4+5`
`y=4x^2-8x+9` This is Standard form.

Answer 2

`y=4x^2-8x+9`

Explanation:

`"the equation of a parabola in "color(blue)"standard form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=ax^2+bx+c ; a!=0)color(white)(2/2)|)))`

`"expand " (x-1)^2" using FOIL"`

`y=4(x^2-2x+1)+5`

`color(white)(y)=4x^2-8x+4+5`

`color(white)(y)=4x^2-8x+9larrcolor(red)" in standard form"`