Select the graph of the quadratic function ƒ (x) = x2 + 3. Identify the vertex and axis of symmetry

To find the vertex of a quadratic function, you need to 'complete the square';

Completing the square gives a quadratic in another form;

For quadratics that have an x² coefficient of 1 as is the case, it is a simple matter to complete the square:

For the quadratic x² + bx + c

Simply, put x added to half the coefficient of the x term (b/2) in a bracket and square the bracket;

Then add the constant (c) and the square of the half the coefficient of the x term (b/2), so:

(x + d) ² + e, where d is a (rational) number to be identified;

d = b/2

e = d² + c

So, for f (x) = x² + 0x + 3:

Then the completed-the-square form is: f (x) = (x + 0) ² + 3

As it happens, this quadratic function has a common normal form and completed-the-square form because the x-coefficient is 0.

The vertex coordinates are, according to the general format given above:

(-d, e).

So, looking at completed-the-square form for the function in question, we can tell the vertex is at the coordinates: (0, 3)

Quadratic functions always have symmetry about the vertical line with the x-coordinate of the vertex;

This makes sense if you think about how the graph looks (u-shaped);

Therefore for our function, the vertex is:

x = 0 (a vertical line with the x-coordinate of the vertex).