# How do you write the standard form equation of the parabola y = 1/2(x - 4)² + 13?

Jun 20, 2018

$y = \frac{1}{2} {x}^{2} - 4 x + 21$

#### Explanation:

$\text{the equation of a parabola in "color(blue)"standard form}$ is.

•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0

$\text{expand "(x-4)^2" and arrange into form}$

$y = \frac{1}{2} \left({x}^{2} - 8 x + 16\right) + 13$

$\textcolor{w h i t e}{y} = \frac{1}{2} {x}^{2} - 4 x + 8 + 13$

$\textcolor{w h i t e}{x} = \frac{1}{2} {x}^{2} - 4 x + 21 \leftarrow \textcolor{b l u e}{\text{in standard form}}$