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

Oct 29, 2016

The standard form of this quadratic function is $y = \frac{3}{4} {x}^{2} - 6 x + 14$.

#### Explanation:

Standard form of a quadratic function is $y = a {x}^{2} + b x + c$. To transform this quadratic function from vertex form to standard form, begin by squaring the binomial. Remember the process of squaring a binomial:

${\left(a + b\right)}^{2}$
$\left(a + b\right) \left(a + b\right)$
${a}^{2} + a b + a b + {b}^{2}$
${a}^{2} + 2 a b + {b}^{2}$

So applying this process to $y = \frac{3}{4} {\left(x - 4\right)}^{2} + 2$ gives us:

$y = \frac{3}{4} \left({x}^{2} - 8 x + 16\right) + 2$

Now, distribute the coefficient $\frac{3}{4}$:

$y = \frac{3}{4} {x}^{2} - 6 x + 12 + 2$

Combine the constants:

$y = \frac{3}{4} {x}^{2} - 6 x + 14$

This is the standard form of the quadratic function.