Question

How do you find the vertex of a parabola `y = x^2 + 3`?

Answer 1

the vertex of `f(x)` is `3` when `x=0`

Explanation:

Let `a,b,c`, 3 numbers with `a!=0`

Let `p` a parabolic function such as `p(x) = a*x^2 + b*x + c`

A parabola always admit a minimum or a maximum (= his vertex).

We have a formula to find easily the abscissa of a vertex of a parabola :

Abscissa of vertex of `p(x) = -b/(2a)`
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Let `f(x)=x^2+3`
Then, the vertex of `f(x)` is when `0/2=0`
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And `f(0) = 3`
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Therefore the vertex of `f(x)` is `3` when `x=0`

Because `a>0` here, the vertex is a minimum.

graph{x^2+3 [-5, 5, -0.34, 4.66]}