# What is the vertex form of  f(x) = -x^2 -x-2 ?

May 18, 2017

The vertex form of equation is $f \left(x\right) = - {\left(x + 0.5\right)}^{2} - 1.75$

#### Explanation:

$f \left(x\right) = - {x}^{2} - x - 2 = - \left({x}^{2} + x\right) - 2 = - \left({x}^{2} + x + {\left(\frac{1}{2}\right)}^{2}\right) + \frac{1}{4} - 2$

$f \left(x\right) = - {\left(x + \frac{1}{2}\right)}^{2} - \frac{7}{4} \mathmr{and} f \left(x\right) = - {\left(x + 0.5\right)}^{2} - 1.75$

Comparing with general vertex form of equation,

f(x) = a(x-h)^2+k ; (h,k)  being vertex, here vertex is at $\left(- 0.5 , - 1.75\right)$

The vertex form of equation is $f \left(x\right) = - {\left(x + 0.5\right)}^{2} - 1.75$ [Ans]