# How do you write the vertex form equation of the parabola  y=-x^2+4x+12?

Feb 12, 2017

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

#### Explanation:

Vertex form of equation is of the type $y = a {\left(x - h\right)}^{2} + k$

Note that here coefficient of ${x}^{2}$ is $a$, hence in $y = - {x}^{2} + 4 x + 12$

we take $a = - 1$. Then we go on to form a square of form ${\left(x - h\right)}^{2}$

$\therefore y = - {x}^{2} + 4 x + 12$

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

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

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

= $- {\left(x - 2\right)}^{2} + 16$