# How do you graph #y=2x^2+12x+16#?

##### 1 Answer

Mar 19, 2018

There is a procedure to graph funcion.

#### Explanation:

- Define the demain and codomain: polynoms are defined everywhere in the real plane (complex too).

#y=2*x^2+12*x+16# - Find the intersection between function and x-axes: solve the equation
#2*x^2+12*x+16=0# | :2

#x^2+6*x+8=0#

Remember:#(a+x)*(b+x)=x^2+(a+b)*x+a*b#

The solution is:#x^2+6*x+8=(x-4)*(x-2)=0# #x_1=4, x_2=2#

[black points] - Calculate the first derivative:
#y'=4*x+12# - Calculate
#y'=0# :

#4*x+12=0# ,#x=-3#

here#(-3,y(-3))=(-3,-2)# blue point the slope change.#(-infty,-3)# the slope is negative (the value of the function fall),#(-3,+infty)# the slope is positive (the value of the function increase). - Calculate the second derivative:
#y''=4#

if#y''>0 # the function is convex (is smiling)

if#y''<0 # the function is concave (is sad)

#y''=4 >0 rArr# is convex

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