Question

Given the parabola f(x) = -(x + 2)2 + 4, find the x-intercept(s).

Answer 1

To find the x-intercepts, plug in f(x) = 0. In other words you replace f(x) with 0.

Then you solve for x


f(x) = -(x + 2)^2 + 4

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


Now solve for x. Let me know if you still need help

Answer 2

wait is it x^2+4x+4

Answer 3

(x + 2)^2

expands out to

x^2 + 4x + 4

Answer 4

So

-(x + 2)^2

expands out to

-(x^2 + 4x + 4)

which distributes to

-x^2 - 4x - 4

Answer 5

This means

-(x + 2)^2 + 4

simplifies to

-x^2 - 4x

Answer 6

how do i get my x-ints from that

Answer 7

We want to solve

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

for x, which is the same as solving

0 = -x^2 - 4x

Answer 8

Which flips to

-x^2 - 4x = 0

Answer 9

Do you see where to go now?

Answer 10

sort of

Answer 11

What do you get when you solve -x^2 - 4x = 0 ?

Answer 12

thats the thing im not quite sure how to solve it would i get x^2=4x or what

Answer 13

Factor as much as you can

Answer 14

or would you take out and x

Answer 15

so factor out -x to get

-x(x + 4) = 0

Answer 16

right

Answer 17

then you can break up

-x(x + 4) = 0

to get

-x = 0 or x + 4 = 0


So you now just need to solve each equation for x

Answer 18

so you get x=-4 and x=0

Answer 19

good you got it

Answer 20

so the x-intercepts as points are (0,0) and (-4,0)

Answer 21

alright im going to post some more could youi help??

Answer 22

sure