# Help plot the following parabola ?

Jun 6, 2018

#### Explanation:

$y = a {x}^{2} + b x + c$

the vertex of quadratic formula given by:

${x}_{v} = - \frac{b}{2 a}$

${y}_{v} = a {\left({x}_{v}\right)}^{2} + b \left({x}_{v}\right) + c$

if a positive the shape of sketch will be $\bigcup$
but if a negative the shape will be $\bigcap$

now lets sketch $y = - {x}^{2} - 2 x + 8$

firstly lets find the vertex:

${x}_{v} = - \frac{b}{2 a} = \frac{2}{-} 2 = - 1$

${y}_{v} = - 1 + 2 + 8 = 9$

$\text{the vertex} = \left(- 1 , 9\right)$

find other points:

$f \left(2\right) = 0$

$f \left(1\right) = 5$

$f \left(0\right) = 8$

$f \left(- 1\right) = 9$

$f \left(- 2\right) = 8$

show below how the sketch will become: