Question

Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the functions based on their axis of symmetry (from smallest to largest).

Answer 1

f(x)
f(x) = –4(x – 8^)2 + 3

g(x)
g(x) = 3x^2 + 12x + 15

Answer 2

h(x)

Answer 3

@jim_thompson5910 can you help me?

Answer 4

@cwrw238
@Loser66

Answer 5

what do you have so far?

Answer 6

I don't know how to do the f(x) and g(x) but I think I get the h(x)

Answer 7

what did you get for the h(x) function

Answer 8

Does it have to be an equation?

Answer 9

yeah the axis of symmetry is an equation of the form x = h where h is some fixed number

Answer 10

I don't know how to do this...

Answer 11

ok forget about the equation, what did you have for h(x) ?

Answer 12

you wrote "I think I get the h(x)"

what did you have in mind?

Answer 13

I was thinking it would be x=3 because that's where axis of symmetry crosses the parabola, but it has to be an equation which I don't know how to do.

Answer 14

it is x = 3 and it's because this is the center line that divides the parabola in half (you can mirror one side over this line to get the other side)

Answer 15

x = 3 is an equation

anything that has an equal sign is an equation

Answer 16

Oh so h(x) would just be x=3?

Answer 17

h(x) is some parabola

we don't really care about the equation for h(x)

but the equation for the axis of symmetry is x = 3 (the axis of symmetry of h(x))

Answer 18

hey I need to go somewhere, i'll tag you when I get back to finish the rest.

Answer 19

ok

Answer 20

I'm back @jim_thompson5910

Answer 21

welcome back

Answer 22

So we got h(x).
How do I do f(x) and g(x) ?

Answer 23

f(x) is really f(x) = -4(x-8)^2 + 3 right?

Answer 24

yup

Answer 25

f(x) = -4(x-8)^2 + 3 is in the form f(x) = a(x-h)^2 + k which is vertex form

Answer 26

what is the value of h?

Answer 27

I just solve the equation to get h?

Answer 28

you really don't need to solve

you just need to compare and line up the numbers with the letters

Answer 29

I got (8,3) for the vertex

Answer 30

the x coordinate of the vertex is what helps determine the axis of symmetry

Answer 31

Axis of symmetry is x = 8

Answer 32

yes

Answer 33

for g(x), I recommend you graph it using a graphing tool like desmos

https://www.desmos.com/calculator

Answer 34

For g(x) I got x=-2 as the axis of symmetry because the vertex is (-2,3)
Is that correct?

Answer 35

correct

Answer 36

So to rank them from smallest to largest it would be
g(x) x=-2 , h(x) x=3, and f(x) x=8
right?

Answer 37

I agree with that order

Answer 38

Thanks for your help!

Answer 39

np