Question

The function below is written in vertex form or intercept form. Rewrite them in standard form and show your work.

y = -3(x-2)(x-4)

Answer 1

The standard form as
`y =-3x^2+18x-24`

Step-by-step explanation:

Given: A function which is written in vertex form or intercept form.

We have to re-write it in standard form that in terms of
`y=ax^2+bx+c`

Given
`y =-3 (x-2)(x-4)`

Multiply each term on the right side, we get,

`y =-3[x(x-4)-2(x-4)]`

`y =-3[x^2-4x-2x+8]`

`y =-3[x^2-6x+8]`

Multiply constant term , we get,

`y =-3x^2+18x-24`

Thus , we have obtained the standard form as
`y =-3x^2+18x-24`

Answer 2

The standard form is: y = -3x² +18x -24.

Explanation:

Given is y = -3(x-2)(x-4)

Using FOIL method to expand the parentheses:-

y = -3(x-2)(x-4)

y = -3(x² -2x -4x +8)

Combining like terms:-

y = -3(x² -6x +8)

Distributing -3 to the terms inside parentheses:-

y = -3x² +18x -24.

Hence, standard form is: y = -3x² +18x -24.