Question

The graph of which function has an axis of symmetry at x = 3? f(x) = x2 3x 1 or f(x) = x2 – 3x – 3 or f(x) = x2 6x 3 or f(x) = x2 – 6x – 1

Answer 1

for
ax^2+bx+c
the axis of symmetry is -b/2a


first one
-3/2=3, nope

2nd one
3/2=3? nope

3rd one
-6/2=3? nope

fourth
6/2=3? yes
answer is last one or
f(x)=x^2-6x-1

Answer 2

Option 4th is correct

`f(x) = x^2-6x-1`

Explanation:

A quadratic equation is in the form of:
`y=ax^2+bx+c`.....[1]; then the axis of symmetry is given by:

`x = (-b)/(2a)`

As per the statement:

To find :

The graph of which function has an axis of symmetry at x = 3

From the given options:

Option 4th is the graph of a function which has axis of symmetry at x = 3

Consider a function:

`f(x) =x^2-6x-1`

On comparing with [1] we have;

a = 1 and b = -6

then;

`x = (-(-6))/(2 \cdot 1)`

⇒
`x = (6)/(2) =3`

Therefore, The graph of which function has an axis of symmetry at x = 3 is,
`f(x) = x^2-6x-1`