Question

What is the axis of symmetry and vertex for the graph `y = -3x^2 + 12x + 4`?

Answer 1

aos = 2

vertex = (2,16)

Explanation:

`y = -3x^2 + 12x + 4`

`f(x) = -3x^2 + 12x + 4`

In the form `y=ax^2+bx+c` you have:

`a=-3`

`b=12`

`c=4`

Axis of symmetry (aos) is: `aos=(-b)/(2a) = (-12)/(2*-3)= 2`

Remember `y=f(x)`

Vertex is: `(aos, f(aos)) = (2, f(2))`:

`f(x) = -3x^2 + 12x + 4`

`f(2) = -3(2)^2 + 12*2 + 4 = 16`

vertex `=(2, 16)`

graph{-3x^2 + 12x + 4 [-16.71, 23.29, -1.6, 18.4]}

Answer 2

Vertex -

`(2,16)`

Axis of symmetry

`x=2`

Explanation:

Given -

`y=-3x^2+12x+4`

Vertex -

`x=(-b)/(2a)=(-12)/(2xx-3)=(-12)/(-6)=2`

At `x=2; y=-3(2^2)+12(2)+4`

`y=-12+24+4=16`

`(2,16)`

Axis of symmetry

`x=2`