Question

What is the end behavior and zeros of f(x) = (x+4)^2

Answer 1

graph it and see

Answer 2

https://www.desmos.com/calculator

Answer 3

Zeroes are when x=0 for the function/graph. To make the function f(x)=0, what does x have to be? End behavior is whether is opens up or down. You shouldn't need to graph this function at all.

Answer 4

for +x^2, the parabola opens up
for -x^2, the parabola opens down

Answer 5

(x + 4)^2 = 0 => x + 4 = 0 => x = -4

Leading coefficient is positive and the function has an even degree so the function is concave up and approaches positive infinity as \(x \rightarrow \pm \infty\). The function also has a zero at \(x=-4\).

@musicalrose

Answer 6

Hi Rose! :o) Like these guys said, whenever you want to find the "zeros" for a function, just set the function equal to zero, then solve for x...that will give you all the points where the function crosses the x-axis, otherwise known as your zeros!

Answer 7

I really simple way to always remember how a function's end behavior works is really easy...if the function is positive and the exponent is even, both sides go up! If the function is still positive but the exponent is odd, then the right side goes up and the left side goes down...something else that's really neat is that if your function has a negative sign in front of it, then just reverse everything...the side that went up when it was positive now goes down, and the side that went down when it was positive, now goes up!

Answer 8

you can also get interactive with it! if you see an x^2, face your graph and stick both arms up in the air! if you see an x^3, facing your graph, stick your right arm up in the air and your left arm down! If your functions are negative, reverse your arms! Super easy that way and it always works...well as far as I have tested anyways! Look at the picture i drew you and you will see how easy it is to always remember the end behavior of ANY FUNCTION! :O) Hope this helpS! Good luck!