Question

Only answer if you're very good at Math.

What is the minimum value of the function g(x) = x^2 - 6x - 12?

A: -21

B: 3-√21

C: 3

D:3+ √21​

Answer 1

A: -21

Explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

`f(x) = ax^(2) + bx + c`

It's vertex is the point
`(x_(v), y_(v))`

In which

`x_(v) = -(b)/(2a)`

`y_(v) = -(\Delta)/(4a)`

Where

`\Delta = b^2-4ac`

If a<0, the vertex is a maximum point, that is, the maximum value happens at
`x_(v)`, and it's value is
`y_(v)`.

In this question:

Quadratic function:

`g(x) = x^2 - 6x - 12`

So
`a = 1, b = -6, c = -12`.

Minimum value:

This is the y-value of the vertex. So

`\Delta = b^2-4ac = (-6)^2 - 4(1)(-12) = 36+48 = 84`

`y_(v) = -(\Delta)/(4a) = -(84)/(4) = -21`

The minimum value is -21, and the correct answer is given by option A.