could someone help me with this problem? f(x) = x^2 +4x + 1?

What is your question?

If you want to plot them, just give a set of x numbers,and compute f(x).

If you want the derivative of f(x), f'(x)=2x+ 4.

If you want the maximum or minimum, set f'(x)=0.

if you want to make a chart using f(x) and x then you simply pick any numbers for x and write them in the first column and you get an answer after you put the value of x into the equation and solve the arithmetic.

For example pick x = 1, 1 would be the first number in the chart and then when you do [1^2 + (4 * 1) +1] you get 6 which will be the second number in the chart.

Hope this helps

Ok, let's see:

x^2 + 4x + 1

for a perfect square you will need,

x^2 + 4x + 4 but this is different from what you have, so, try the following:

x^2 + 4x + 4 + 1 - 4 (you add 4 and subtract 4...that's the trick!)

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

Hope this helps!

f(x) = x^2 + 4x + 1 . . . . . . is similar to y = x^2 + 4x + 1

y = x^2 + 4x + 2^2 + 1 - 2^2

y = ( x + 2)^2 -3

y + 3 = ( x + 2)^2 . . . . . this is a parabola with vertex (-3, -2) facing up

intercept at (-2+sqr(3), 1)

What do you want with this function? Graph, tangent lines, intercepts, etc.?