# How do you sketch the graph of y=(x+3)^2 and describe the transformation?

May 6, 2018

#### Explanation:

show below

$y = {\left(x + 3\right)}^{2}$

$y = {x}^{2} + 6 x + 9$

we will compare the above function with this below

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

we will get

$a = 1 , b = 6 \mathmr{and} c = = 9$

now we will find the vertix

${x}_{v} = - \frac{b}{2 a} = - \frac{6}{2} = - 3$

${y}_{v} = {\left(- 3\right)}^{2} + 6 \left(- 3\right) + 9 = 0$

use some points to simplify the sketch

$f \left(2\right) = 25$

$f \left(1\right) = 16$

$f \left(0\right) = 9$

$f \left(- 1\right) = 4$

$f \left(- 2\right) = 1$

now the sketch of our function $y = {x}^{2} + 6 x + 9$

graph{x^2+6x+9 [-12.42, 10.08, -2.44, 8.81]}