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)=-4(x-8)^2+3

g(x) = 3x2 + 12x + 15

Answer 2

@issaiahphillips

Answer 3

The axis of symmetry is a vertical line with the equation of x = -b/2a.

Start by getting f(x) into a simpler form. Something like ax^2+bx+c

Answer 4

from my thoughts the biggest is f and the smallest is g and h is in the middle

Answer 5

Yeah i got that its just finding the axis of symmetry that is getting me stuck. @issaiahphillips

Answer 6

ooooh ok gotcha workin in it

Answer 7

that's wrong @issaiahphillips

I repeat, the axis of symmetry is a vertical line of form -b/2a

so taking g as an example, the axis of symmetry is x=-12/6=-2

Answer 8

The axis of symmetry is a vertical line that passes through the vertex.
f(x) = -4(x - 8)^2 + 3 is already given in the vertex form.
Vertex is (8, 3)
So the axis of symmetry for f(x) is: x = 8

Answer 9

g(x) is given in the standard form: ax^2 + bx + c
The axis of symmetry is: x = -b/(2a)

Answer 10

I just need h(x) i'm stuck on it @aum

Answer 11

Identify the vertex from the graph.

Answer 12

is the vertex (3,2)?

Answer 13

Yes. The axis of symmetry is a vertical line that passes through the vertex.

Answer 14

So then the axis of symmytry would be 3?

Answer 15

The equation is: x = 3

Answer 16

x = constant is the equation of a vertical line.
y = constant is the equation of a horizontal line.

Answer 17

Thank you! @aum

Answer 18

You are welcome.