Question

I got this question wrong and I don't understand it....please explain

What are the coordinates of the vertex for f(x) = x^2 + 4x + 10?

A) ( -2, 2)
B) ( 2, 2)
C) ( -2, 6)
D) ( 2, 6)

Answer 1

Option C (-2, 6)

Explanation:

Let
`f(x) = ax ^ 2 + bx + c` the equation of a parabola, with a, b, c real numbers. So the vertex of this function is:

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

In this case, the parable is:

`f(x) = x^2 + 4x + 10`

Thus:

`a = 1\\b = 4\\c = 10`

So the vertex of this parable is:

`x = -(4)/(2(1))\\\\x = -2`

We know that the vertex of this parable is at the point

`x = -2\\\\y = f(-2)\\\\y = f(-2) = (-2) ^ 2 +4 (-2) +10\\\\y = 4 - 8 +10\\\\y = 6`

Finally the vertex is at the point (-2.6)

The correct option is: C (-2, 6)