Question

How do you write in standard form `y=3/4(x-4)^2+2`?

Answer 1

The standard form of this quadratic function is `y = 3/4x ^2 - 6x + 14`.

Explanation:

Standard form of a quadratic function is `y = ax^2 + bx + c`. To transform this quadratic function from vertex form to standard form, begin by squaring the binomial. Remember the process of squaring a binomial:

`(a + b)^2`
`(a + b)(a + b)`
`a^2 + ab + ab + b^2`
`a^2 + 2ab + b^2`

So applying this process to `y = 3/4(x - 4)^2 + 2` gives us:

`y = 3/4(x^2 - 8x + 16) + 2`

Now, distribute the coefficient `3/4`:

`y = 3/4x^2 - 6x + 12 + 2`

Combine the constants:

`y = 3/4x^2 - 6x + 14`

This is the standard form of the quadratic function.