# How do you write the quadratic function in standard form y=-1/2(x-6)(x-8)?

Apr 3, 2017

$7 x - {x}^{2} / 2 - 24$

#### Explanation:

Let's first multiply $\left(x - 6\right) \left(x - 8\right)$. We will use FOIL to expand this (first, outer, inner, last).

First: $x \cdot x = {x}^{2}$
Outer: $x \cdot - 8 = - 8 x$
Inner: $x \cdot - 6 = - 6 x$
Last: $- 8 \cdot - 6 = 48$

Add these all up to get ${x}^{2} - 14 x + 48$.

Now, don't forget to multiply each of these terms by $- \frac{1}{2}$ to get $- {x}^{2} / 2 + 7 x - 24$. We can arrange the terms so that the positive term is in the front $7 x - {x}^{2} / 2 - 24$.