Question

What is the axis of symmetry and vertex for the function f(x) = 3(x – 2)2 4?

Answer 1

Hello,

y=3(x-2)²+4

Vertex is(2,4)
Axis of symmetry: x=2

Answer 2

we know that

The equation of a vertical parabola in vertex form is equal to

`y=a(x-h)^(2)+k`

where

(h,k) is the vertex

if
`a > 0` -----> then the parabola open upward (the vertex is a minimum)

if
`a < 0` -----> then the parabola open downward (the vertex is a maximum)

The axis of symmetry is equal to

`x=h`

In this problem let's analyze two cases

First case

`f(x)=3(x-2)^(2)+4`

the vertex is the point
`(2,4)`

`a=3`

so

`3 > 0` -----> then the parabola open upward (the vertex is a minimum)

The axis of symmetry is equal to

`x=2`

Second case

`f(x)=3(x-2)^(2)-4`

the vertex is the point
`(2,-4)`

`a=3`

so

`3 > 0` -----> then the parabola open upward (the vertex is a minimum)

The axis of symmetry is equal to

`x=2`