Question

How do you write the quadratic function in standard form `y=-2(x+4)(x-3)`?

Answer 1

`f(x) = y= -2x^2-2x+24`

In Standard form: `-2x^2-2x-y+24=0`

Explanation:

The given expression has been factored already, which will be helpful in solving for the unknown values `x and y`.

But this time the question is how to write the equation back into its standard form.

Standard form of a quadratic function requires the expression to contain terms with the highest exponents written first.

We will need to re-multiply the factors to obtain the equation.
to do this we can use the `FOIL*FOIL` method. We call it this because it means multiply (First)(First), (Outer)(Outer), (Inner)(Inner), and (Last)(Last).

We can calculate the signs according to the multiplication then addition and subtraction of the terms as necessary.

`y= -2(x+4)(x-3)` where we want to start with brackets only

(F)(F): `(x ..)(x ..) = x^2; ...(O)(O):(x)(-3) = -3x;`

`(I)(I): (4)(x)= 4x; ... (L)(L):(+4)(-3) = -12`

We can then substitute these values back into the original equation.

`y=-2(x^2-3x+4x-12)`

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

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

In Standard form: `-2x^2-2x-y+24=0`