Question

Given the functions f(x) = x2 + 6x − 1, g(x) = –x2 + 2, and h(x) = 2x2 − 4x + 3, rank them from least to greatest based on their axis of symmetry.

Answer 1

Treat them as if you were completing the square

Answer 2

so\[x^2+6x-1=(x+3)^2-10\], the bracket sets them up looking like an a^2-10 (a=x+3), like any normal quadratic they start at a line of symmetry of x=0, so the translation of -10 means is irrelevant and the transformation +3 means the line of symmetry shifted to the left by 3 (i.e line of symmetry is x=-3)

Answer 3

Try it for the rest then you can compare their lines of symmetry

Answer 4

I see!

Answer 5

so for the 2nd one, take out the the negative. -x^2+2=-(x^2-2), line of symmetry is x=2

Answer 6

Yep! I understand now. Thank you so much!

Answer 7

Whoops, I've run into some trouble again.

When comparing the line of symmetry for h(x), which I found to be positive 1, I realized it can't be the right answer.

What am I doing wrong?

Answer 8

@14mdaz

Answer 9

so factorising 2 out \[2x^2-4x+3=2(x^2-2x)+3=2(x-1)^2-1+3\] line of symmetry should be positive 1

Answer 10

oh after the 2 should still be 2(((x-1)^2)-1) but that still wouldnt make a difference to the line of symmetry

Answer 11

Exactly! However, according the practice module, that can't be right. Is there a possibility that f(x) is equivalent to positive 3 rather than negative as we had originally thought?

Answer 12

its still gonna be +3 in the brackets so thats a -3 translation, did you type up f(x) wrong?

Answer 13

Well, in the practice module, it gave these options for the ordering of the functions by line of symmetry (least to greatest):

Answer 14

A. f, g, h

Answer 15

B. h, g, f
C. g, h, f
D. h, f, g

Answer 16

so it should be in the order (small to greatest), f(x), h(x), g(x) :/

Answer 17

But our findings would suggest f, h, g, like you said, but it's not an option.

Answer 18

It must be an error in the module.

Answer 19

oh sorry i made a mistake with g

Answer 20

you dont need to bracket it because its -x^2, its an upside down quadratic so its symmetry is still 0 not 2

Answer 21

thus the order would be f, g, h?

Answer 22

yes

Answer 23

Thank you for clearing that up! I was driving myself crazy. It's funny that I didn't notice the error in g(x) either.

Answer 24

it was my fault i thought -(x^2-2) was -(x-2)^2 XD