How do you write the function in standard form y=-3(x-7)(x+4)?

Feb 10, 2017

To write this in standard form we need to multiply the two terms in parenthesis on the right side of the equation.

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$y = - 3 \left(\textcolor{red}{x} - \textcolor{red}{7}\right) \left(\textcolor{b l u e}{x} + \textcolor{b l u e}{4}\right)$ becomes:

$y = - 3 \left(\left(\textcolor{red}{x} \times \textcolor{b l u e}{x}\right) + \left(\textcolor{red}{x} \times \textcolor{b l u e}{4}\right) - \left(\textcolor{red}{7} \times \textcolor{b l u e}{x}\right) - \left(\textcolor{red}{7} \times \textcolor{b l u e}{4}\right)\right)$

$y = - 3 \left({x}^{2} + 4 x - 7 x - 28\right)$

We can now combine like terms:

$y = - 3 \left({x}^{2} + \left(4 - 7\right) x - 28\right)$

$y = - 3 \left({x}^{2} - 3 x - 28\right)$

We can now multiply each term in parenthesis by $- 3$:

$y = \left(- 3 \times {x}^{2}\right) - \left(- 3 \times 3 x\right) - \left(- 3 \times 28\right)$

$y = - 3 {x}^{2} + 9 x + 84$