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

Mar 30, 2017

$f \left(x\right) = y = - 2 {x}^{2} - 2 x + 24$

In Standard form: $- 2 {x}^{2} - 2 x - y + 24 = 0$

#### Explanation:

The given expression has been factored already, which will be helpful in solving for the unknown values $x \mathmr{and} y$.

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 $F O I L \cdot F O I L$ 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.

$y = - 2 \left(x + 4\right) \left(x - 3\right)$ 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.

$y = - 2 \left({x}^{2} - 3 x + 4 x - 12\right)$

$y = - 2 \left({x}^{2} + x - 12\right)$

$y = - 2 {x}^{2} - 2 x + 24$

In Standard form: $- 2 {x}^{2} - 2 x - y + 24 = 0$