Question

f(x)=2(x+2)(x+2)-3

Answer 1

What are you being asked to do?!

Answer 2

to sketch the graph of each function

Answer 3

what is "each" function? if im interpreting this correctly, your only function is \[f(x)=2(x+2)(x+2)-3\]
which simplifies to \[f(x)=2x^2+6x+5\]

Answer 4

this is in quadrtic form of a parabola, so
a=2
b=6
c=5.

if you were to find the axis of symettry first, it would be
\[\frac{ -b }{ 2a }\]

Answer 5

so the axis of symetry is -6/4 = -3/2.

Answer 6

and now you can plug in that x=-3/2 into the quadratic to find y and there you have the vertex.

Answer 7

notice how your a is positive,

if a>0 the parabola is up, which mean they have a minimum
if a<0 the parabola is down, which means they have a maximum.

Answer 8

and simply plug in 0 in for x and generate another point on the parabola, and this parabola has a line of symmetry so you can relate that point and get another point. 3 points create a parabola!

Answer 9

when you simplify where did you get the "6x"from?

Answer 10

lets do this one step at a time then.
f(x)=2(x+2)(x+2)−3

f(x)=(2x+4)(x+2)-3
2x^2 + 4x +4x +8 - 3.

sorry about that, its actually 8x

Answer 11

so will my final answers look like this? -3.2 and -0.8

Answer 12

so then it is \[2x^2+8x+5\]

Answer 13

what do you mean by final answer, arent u graphing the function?

Answer 14

it will look somewhat like this