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) = 3(x + 4)2 + 1

Answer 2

g(x) = 2x2 −16x + 15

Answer 3

Can someone help?

Answer 4

@phi

Answer 5

For the first one, you can find the vertex (p,q) because it is in vertex form y=a(x-p)^2+q

Answer 6

(4,1)

Answer 7

The second one you have to complete the square:
g(x)=2x^2-16x+15
g(x)=2(x^2-8x)+15
g(x)=2[(x^2-8x+16)-16}+15
g(x)=2(x-4)^2-17

Answer 8

your vertex is wrong

Answer 9

how?

Answer 10

well i said the vertex form is y=a(x-p)^2+q, if you plugged in (4,1), the vertex form will be
y=3(x-4)^2+1

Answer 11

So change the sign of the x coordinate

Answer 12

(-4,1)

Answer 13

Exactly, did you find the vertex for g(x)?

Answer 14

the second one is (4,1)7

Answer 15

(4,17)

Answer 16

right

Answer 17

But what about the third one?

Answer 18

and for the last one, just look fot the coordinate that is either the maximum or minimum

Answer 19

minimum is (1,-3)

Answer 20

In this case, the vertex is the minimum value so what is the coordinate that is the lowest point?

Answer 21

right

Answer 22

and the axis of symmetry?

Answer 23

how do i find that again?

Answer 24

hello?

Answer 25

x=-b/2a

Answer 26

oh shoot, I re-read your question, i showed you how to find the vertex.

Answer 27

ok, so let's restart

Answer 28

lol

Answer 29

you need to convert f(x) into a quadratic equation, so
f(x) = 3(x + 4)^2 + 1
f(x)=3(x^2+8x+16)+1
f(x)=3x^2+24x+49

Answer 30

now that its a quadratic equation (ax^2+bx+c), a is 3 and b is 24

Answer 31

plug it into the axis of sym. formula -b/2a and you'll have -24/3*2

Answer 32

that's -24 divided by 6, which is -4, and that is the axis of sym.

Answer 33

g(x) is already a quadratic equation so what would a and b be?

Answer 34

-8

Answer 35

err, not exactly, a is 2 and b is -16, so try again

Answer 36

-4 my bad lol

Answer 37

its ok

Answer 38

the axis of sym for the graph is pretty easy to find, it's just the x-coordinate of the vertex which we found earlier

Answer 39

(1,-3)

Answer 40

1

Answer 41

right

Answer 42

so wait in order from biggest to smallest would be f(x), g(x) and the graph?

Answer 43

correct?

Answer 44

well f(x)'s aos = g(x)'s aos so im not sure if you want to specify that they're equal to each other

Answer 45

but the graph's aos is a positive number while the other two are negative, so do you think it would be the smallest?

Answer 46

lol, can you show me how to find each axis of symmetry again :)

Answer 47

dude i spent literally spent 20 minutes explaining, all I can say is x=-b/2a is used to find the aos. As long as the function is quadratic, it is pretty easy to figure it out

Answer 48

I know and thx so much :)