Question

Axis of symmetry f(x) =x^2 +3X + 6

Answer 1

Axis of symmetry:
`\sf x = -(3)/(2) \textsf{ or } - 1.5`

Explanation:

The axis of symmetry for a quadratic function in the form
`\sf f(x) = ax^2 + bx + c` can be found using the formula:

`\sf \textsf{Axis of Symmetry} = (-b)/(2a)`

For the given quadratic function
`\sf f(x) = x^2 + 3x + 6`, the coefficients are
`\sf a = 1`,
`\sf b = 3`, and
`\sf c = 6`.

Now, Substitute these values into the formula:

`\sf \textsf{Axis of Symmetry} = (-3)/(2(1))`

Simplify the expression:

`\sf \textsf{Axis of Symmetry} = -(3)/(2)`

So, the axis of symmetry for the quadratic function
`\sf f(x) = x^2 + 3x + 6` is
`\sf x = -(3)/(2) \textsf{ or } - 1.5`.