How do you find the vertex of f(x)=x2+3?

1 Answer
Apr 25, 2016

(0,3)

Explanation:

The equation of a parabola (with vertical axis) in vertex form can be written:

f(x)=a(xh)2+k

where (h,k) is the vertex and a0 a constant multiplier.

In our case we find:

f(x)=1(x0)2+3

which means that (h,k)=(0,3) and a=1

So the vertex is (0,3)


Alternatively, note that x20 with minimum value 0 only when x=0. Hence the minimum value of f(x) is also when x=0. So the x coordinate of the vertex must be 0.

Substituting x=0 in the formula for f(x) gives us f(0)=3.

Hence the vertex is at (0,3)