Question

https://cdn.ple.platoweb.com/EdAssets/560702b9dc1348a5974f50f34a330372?ts=635361559291470000

The graph represents the function f(x) = x2 + 3x + 2.

If g(x) is the reflection of f(x) across the x-axis, g(x) = . (Write the function in standard form. Use ^ to indicate an exponent.)

Answer 1

hint: if you reflect f(x) over the x axis to get g(x), then g(x) = -f(x)

Answer 2

im still confused haha

Answer 3

let's say f(x) = x^2 - 6x + 10

multiply both sides by -1 to get

-1*f(x) = -1*(x^2 - 6x + 10)

-1*f(x) = -1*x^2 -1*(-6x) - 1*10 ... distribute

-f(x) = -x^2 + 6x - 10

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If you compare f(x) = x^2 - 6x + 10 to -f(x) = -x^2 + 6x - 10, you'll find that all of the signs have been flipped. Eg: +x^2 goes to -x^2 or -6x turns into +6x

So if f(x) = x^2 - 6x + 10, and we flip it over the x axis to get g(x), then

g(x) = -f(x)

g(x) = -x^2 + 6x - 10

this isn't the answer as it's just an example

Answer 4

so then would i do g(x)=x^2 + 3x + 2?

Answer 5

that's f(x)

to find g(x), you simply swap all of the signs on f(x)

Answer 6

so then it would be g(x)=x^2-3x-2?
right? sorry im pretty bad at algebra

Answer 7

don't forget about the first term x^2

Answer 8

so that needs to have a negative sign in front of it also?

Answer 9

yes because in f(x), the x^2 is like +x^2

Answer 10

oh okay haha so then what do i do next?

Answer 11

the +x^2 just turns into -x^2

Answer 12

you had the other parts correct

Answer 13

okay then what do i do?

Answer 14

so what I'm saying is that f(x) = x^2 + 3x + 2 turns into g(x) = -x^2 - 3x - 2

Answer 15

all of the signs flip

Answer 16

and thats the answer?

Answer 17

yeah

Answer 18

oh okay thanks

Answer 19

np